Yes. The reasons are technical and have to do with creation of the two different kinds of sheetstock, and specifically bonding.
It is very difficult to bond SS directly to copper, just as it is to bond SS to pure aluminum. Falk’s 1983 process patents solved the former problem (and was licensed to all the other makers of the copper bimetal), but there are limits on forming copper bimetal pans with lining layers thicker than those used. For example, Falk used to disclose that its stockpots cost so much because fully 40% were defective out of the 80-ton press–something in the bimetal sheet breaks in the stretching.
If you research clad, what you find is that the “sandwich” is a very carefully-chosen mix of material layers which will bond well, be formable, and stable. This is the #1 explanation (dirty secret, really) of the reason for multi-layer clad. You can have your high-purity aluminum or copper core, but it needs something between it and the SS–usually a lower-purity aluminum. Demeyere and others used to brag about silver in their sandwiches, but it has zero to do with performance, and everything to do with bonding and forming. Adding an induction layer complicates matters even further.
Falk’s sheetstock is formed under great heat and 850T of pressure, and would be impossible without proprietary heat resistors. It results in an intercrystalline structure that is not present in clad. While All-Clad’s triply is made at about 1000F for reasons of ductility and bond strength, the process of roll-bonding can be done at room temperature. But the SS needs to be thicker.