There are several reasons for being so sure on this point. First of all, this earth is also declared to be the final home for the righteous.
Your assumption that the wicked will be punished on this earth and therefore the wicked must be burned up (according to you) so that the believers can live afterward on this planet is deeply flawed to say the least. This earth is not the home of the believer - it never has been. The believe is a sojourner here - the elect reside as foreigners - for the land of promise given as our eternal home is Jerusalem. No, not some city in the middle-east, not that Jerusalem which was but a type. That eternal city has a builder and maker which is God - it is not this earth.
By faith he resided as a foreigner in a land of promise, living in tents with Isaac and Jacob, the joint-heirs of the same promise; for he looked forward to a city having the foundations of which the builder and maker is God. (Heb 11:9-10)
Abraham looked forward to the day when he would reside in that heavenly city. There is nothing eternal on this earth - this earth will be destroyed by fire on that last day. Our eternal city wherein righteousness dwells in a city yet to be.
For we do not have here a continuing city, but we seek the city coming. (Heb 13:14)
The earth and the heavens and all that is in them will be dissolved - they will be gone! So, our heavenly city is not on this sin-cursed earth, that is not the coming city.
But the day of the Lord will come like a thief, and then the heavens will pass away with a roar, and the heavenly bodies will be burned up and dissolved, and the earth and the works that are done on it will be exposed. Since all these things are thus to be dissolved, what sort of people ought you to be in lives of holiness and godliness, waiting for and hastening the coming of the day of God, because of which the heavens will be set on fire and dissolved, and the heavenly bodies will melt as they burn! (2Pe 3:10-13)
The believers, like Abraham, are waiting by faith for the New Heavens and a New Earth! It is a new creation - this present universe is gone. That is our eternal heavenly city - the New Jerusalem (which spiritually will be the City of Peace).
But according to his promise we are waiting for new heavens and a new earth in which righteousness dwells. Therefore, beloved, since you are waiting for these, be diligent to be found by him without spot or blemish, and at peace. (2Pe 3:10-14)
The New Heaven and New Earth are not the same as the first earth - which has passed away, they are new creations unlike the old. You can remove that stumbling stone then - for the wicked do not have to be burned up in order to make way for the habitation of the believers on this earth. This earth is gone, and the heavens - it has all passed away forever.
Then I saw a new heaven and a new earth, for the first heaven and the first earth had passed away, and the sea was no more. And I saw the holy city, new Jerusalem, coming down out of heaven from God, prepared as a bride adorned for her husband. And I heard a loud voice from the throne saying, "Behold, the dwelling place of God is with man. He will dwell with them, and they will be his people, and God himself will be with them as their God. (Rev 21:1-3)
On to your next error - are the unbelievers burned up on the earth and also gone forever? Notice that after God describes the New Earth and Heavens and that this is our new eternal home - He says:
But nothing unclean will ever enter it, nor anyone who does what is detestable or false, but only those who are written in the Lamb's book of life. (Rev 21:27)
How could anyone who is unclean - that is, unredeemed, enter the city if they no longer exist, if they are all were burned up in the consuming fire that destroyed the earth? Well, we just need to read a bit further:
Blessed are those who wash their robes, so that they may have the right to the tree of life and that they may enter the city by the gates. Outside are the dogs and sorcerers and the sexually immoral and murderers and idolaters, and everyone who loves and practices falsehood. (Rev 22:14-15)
Those that are washed in Christ's blood and wear His symbolic robe of covering - they have spiritually eaten of the Tree of Life - which is Christ, and have eternal life. These are the only ones allowed to enter into the symbolic gates of the Kingdom of God and abide in the New Heavens with Christ. And who are those that are OUTSIDE the blessing of God and receive none of these things? Why, it is none other than the unregenerate who you have erroneously decided to burn up with the earth.
But they aren't turned to ash are they? They exist - outside the city - and they aren't permitted into the city, that is, they have no part in the future blessings that God will bestow on those He loves.
You do err in this - for God is not mocked! The unbelievers continue to exist - and in torment they are thrown out of the presence of God. Those that recline at table with Abraham, are those that have the faith of Abraham - i.e., a living faith given by God. These are the believers that abide in the Kingdom of Heaven. For the ungodly, they exist in outer darkness (not on the earth mind you), and suffer with much weeping over their eternal state.
I tell you, many will come from east and west and recline at table with Abraham, Isaac, and Jacob in the kingdom of heaven, while the sons of the kingdom will be thrown into the outer darkness. In that place there will be weeping and gnashing of teeth." (Mat 8:11-12)
The wicked are put "in that place" - which is called outer darkness, where they gnash their teeth. Not for a few moments and then are no more as you propose. In order to put the wicked in their place there must first come a Judgment - a separation of the just from the unjust.
Before him will be gathered all the nations, and he will separate people one from another as a shepherd separates the sheep from the goats. And he will place the sheep on his right, but the goats on the left. (Mat 25:32-33)
What happens to the elect - His sheep, the ones God chose to save from their sins? They enter into that Heavenly City - the New Jerusalem, and abide eternally with Christ, as we have already seen.
Then the King will say to those on his right, 'Come, you who are blessed by my Father, inherit the kingdom prepared for you from the foundation of the world. (Mat 25:34)
What happens to the non-elect - the goats, the ones God did not choose? Just as we've already read - they are cast out into eternal fire, a place of habitation outside the eternal City, a place that God also prepared for those that are cursed.
"Then he will say to those on his left, 'Depart from me, you cursed, into the eternal fire prepared for the devil and his angels. (Mat 25:41)
In case you are still tempted to wiggle away from the truth God is presenting -- Jesus repeats their fate again:
And these will go away into eternal punishment, but the righteous into eternal life." (Mat 25:46)
The nature of the punishment is - eternal. The nature of the life for the righteous is - eternal. Same word! There are two groups, goats and sheep, one Judgment at the end of the world, and two destinations: abide in the New Heavens or abide in Outer Darkness. Both are eternal, never ending, everlasting abodes.
As much as men want to rid God of the unrighteous by burning them up - God will not allow it. The wicked offended an eternal God - and so they pay an eternal price, in an eternal punishment. We are all by nature eternal - which is why it is serious matter as to which kingdom we belong: Christ's or Satan's. Apart from Christ taking our eternal punishment for us, we would join the wicked in eternal torment apart from God outside the Holy City, forever in darkness. But, Christ is God, and can pay our eternal debt in finite time - whereas we cannot.
And this is the promise which He promised us: everlasting life. (1Jn 2:25)
This is why it is so fearful to fall into the hand of God. There is something to fear. Those that torture Scripture to avoid the eternal torment of the unrighteous stand alone - for in opposing God they out of their own minds seek to negate what God has spoken. Yet, God has spoken and He will bring it to pass.
And the smoke of their torment goes up forever and ever. And those worshiping the beast and its image have no rest night and day, even if anyone receives the mark of its name. (Rev 14:11)
For those that are interested, the Beast is a typology to represent the unreasoning mind of man - that is like unto a beast. The Beast is the unregenerate, wicked man who worships his father Satan. They carry the mark, or ownership, of their master, just as the believers are marked by God as His possession. Again, two groups or families - God's and Satan's. Each with two different eternal destinations. Best to take it seriously.
Distant ones, hear what I have done; and you near ones, know My might. The sinners of Zion are afraid; terror has seized profane ones; who of us shall tarry with consuming fire? Who of us shall tarry with everlasting burnings?
He who walks righteously and speaks uprightly; he who despises the gain of oppressions, who shakes his hands free from taking the bribe, who stops his ear from hearing of blood, and shuts his eyes from looking at evil. He shall live on high; strongholds of rocks will be his retreat; his bread shall be given; his waters are faithful. Your eyes shall see the king in his beauty; they shall see a land that is very far off. (Isa 33:13-17)
Two groups of people:
The wicked are ordained to the consuming fire - the Lake of Fire, which is the second death. The first death is the separation of our body from our soul - the second death is the separation of ourselves from God's Spirit and all His blessings, it is to be cast out - a death that is eternal. Thus is recorded an everlasting burning - not because the fire burns nothing forever - but because the fire burns the wicked forever. The smoke of their torment ascends forever, not as you suppose in some fashion after they are long gone or turned to ash, but because they are still present and in torment for ever - an everlasting destruction from the face of the Lord!
And to you who are troubled rest with us, when the Lord Jesus shall be revealed from heaven with his mighty angels, In flaming fire taking vengeance on them that know not God, and that obey not the gospel of our Lord Jesus Christ: Who shall be punished with everlasting destruction from the presence of the Lord, and from the glory of his power; (2Th 1:7-9)
The believer shall find refuge in the "strongholds of rocks", which is Christ the Rock, and shall eat the Bread and Water of Life, which again is Christ. Thus, the righteous also continue forever - in their abode with Christ in the New Heavens and New Earth.
No one like the idea of the wicked enduring a punishment that last forever - but when we are with God in heaven, then we'll understand the Holiness of God more fully, and then fully understand how abhorrent sin is to God. We'll know just what it means to offend an eternal God who is angry forever. That will be our reminder of the great price that Christ had to pay.
And indeed, if Christ paid that eternal price on the behalf of the elect - you can be certain the wicked WILL pay too - to the last cent it paid - a time period that will never be obtained. Only Christ could pay the utmost farthing and redeem us from the wrath of God. Thus, the matter is eternally weighty and should make us fearful that we adjudge ourselves circumspectly - lest we be found as unfaithful servants upon His return.
And if anyone was not found having been written in the Book of Life, he was thrown into the Lake of Fire. (Rev 20:15)
And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever. (Rev 20:10)
For this reason we beseech men that they turn from their sins and beg God for mercy in the here and now. What to worry if the wicked are but in a moment burned up - but what to worry knowing that God is a consuming fire that will unleash His eternal wrath upon the wicked forever and ever!
Seek ye the LORD, all ye meek of the earth, which have wrought his judgment; seek righteousness, seek meekness: it may be ye shall be hid in the day of the LORD'S anger. (Zep 2:3)
john