Some people have expressed concern about the copper on copper bottom pans melting onto flat-top stoves.
From a purely physical perspective, this seems unlikely, as the melting point of copper is about 2000 degrees Fahrenheit and if a stove got that hot, you would have bigger problems than your cookware melting.
However, searching the Internet brings up plenty of examples of people complaining of just that.
This tip for glass cooktops might explain what is happening:
“If using copper cookware, make sure that there is no tarnish on the bottom of the pan, otherwise it will stain the cooktop.”
I have seen copper flake off on a gas stove when I was deliberately trying to overheat a pan for a test.
It is possible that even a slight amount of tarnish could come off and stick to the stove top.
Additionally, Revere Ware can be problematic on flat-top stoves as they are prone to warping from misuse, such as if they are overheated or put under cold water when hot. Even a slight warp can make them unsuitable for flat-top stoves.
I would say the risks outweigh the benefits of using Revere Ware copper bottom pans on a flat-top stove.
However, there is one type of Revere Ware that we like a lot that would be better for flat-top stoves: Tri-Ply.
This type has an aluminum core on the bottom sandwiched between stainless steel and works very well at spreading out the heat, like the copper bottom does, and will be less likely to warp. You can probably buy a set for a mere fraction of what you might pay for All-Clad, which uses the same technology although throughout the entire pot, not just on the bottom.
There is a fair amount of Revere Ware Tri-Ply cookware available on Ebay.