So AMD might need a hardware solution for FSR 3 to work.
It seems unlikely that you would need specialized hardware for frame generation to work, though having access to it might improve performance at a given quality level. Even without dedicated hardware, as long as the frame generation calculations take significantly less time to perform than rendering a new frame, the feature could be beneficial.
It sounds a lot like the frame-doubling used to reduce performance drops on VR headsets, like "Asynchronous Spacewarp" for Oculus, a feature that they added through a software update six years ago. That just looks at the previous frame's depth and motion vector buffers and uses that information to deform the frame to simulate a new one, shifting objects to their new, estimated positions. There can be artifacts in some scenarios though, since missing regions behind moving objects need to be filled in, and I wouldn't expect either Nvidia or AMD's solutions to look perfect either, but it could be an effective way to make low frame rates feel a lot smoother.
Maybe Nvidia thinks they can sell more graphics cards by artificially restricting the feature to 40-series hardware, but I see little reason why such a feature couldn't be enabled on all cards.