Maybe not, but when people were pulling the silver out of circulation back in the 1960's each of those coins was only worth a couple cents over face value, just like the copper cents today. Just a couple cents over face. Of course with the silver coins it took about 7 years before the coins were worth three times face. The copper cents are already at that point.
Copper was pulled from cents in 1982, 28 years ago. It's taking a lot longer than 7 years for copper to become worth the time of pulling out of circ.
Unlike the case with silver in the '60s, where just about everyone, it seems, knew that the silver was being removed from the dimes and quarters (and thus they were saving all the silver coins they could, even the 40% halves), and it was easy to tell the old silver coins from the new clad coins, the removal from copper from the penny passed with little fanfare in the early '80s, and a lot of people even today think that the cent is still made of copper because the new zinc cents are virtually indistinguishable by the naked eye from the older copper (bronze) cents. Of course, copper is not a "precious metal" either, and until recently was valued at a tiny premium over the content of the cent, so there wasn't much of an incentive to pull copper cents from circulation if they were common dates.