I hunt old-town urban demo's with a "relic" mindset . Ie.: dig all above iron. However, I have encountered some that did require a bit more cherry-picking, because like ..... if they were filled with tabs and foil or whatever (to keep from going crazy, I had to pick my priorities).
An example of this: they tore down the grandstands of our local rodeo grounds in the mid 1990s. These were built in the 1920s, and underneath them, had been hard-pan ground terra-firma. You can imagine the coin bonanza it was when they starting dozing around the ground beneath these bleachers (all those years of people fiddling with their coins in the slatted seating above, to buy sodas and hot-dogs all those years from the roving concessioners). But you can also imagine the sea of tabs as all those beer and soda drinking attendees had merely stuck all their trash through the open slatted seating too! (they clean out all the standing trash after each event from below, but all the ocean of smaller tabs and stuff was still there). If we had thought we were gonna be heros and get nickels in that sea of tabs and foil would have been fool-hearty indeed! The places was slated to be filled with fill-dirt in a matter of days, so we had to make haste and get all the silver, wheaties, etc... A person would have gone mad if he hadn't cherry picked in a situation like that. So it all just depends on the type site.
If you're dealing with sites where all the surface newer stuff has been scraped off, or if you simply have time to strip-mine, then sure, dig all except iron.