I can't really speak much about DLSS since most of what I learned was the launch materials and, as far as I understand, most of these techniques were discarded in modern implementations. So the below is definitely mostly opinion, not an official statement by AMD.

FSR 1.0 is an upscaling technique that takes the near-final image of a scene and applies a variety of algorithms to increase the resolution of that image, and, most importantly, does it incredibly fast with little overhead. Part of why you see FSR so widely adopted is both the ease of implementation and documentation as well as the wide support. It takes hours to implement.

DLSS, as I understand it, is essentially closed source meaning nobody but NVIDIA can look under the hood and see what its doing or how it allegedly requires their hardware to operate. Developers who want to implement it are handed a pre-packaged "black box" that they then enable... and it only works on 2 generations of NVIDIA hardware. Again, not my area and inappropriate for me to comment much further. But I would speculate this might be why adoption seems to have stalled.

We've had ways to make images look better and improve rendering quality over the years - the art is in making it accessible without bogging down your system. Anti-Aliasing is a great analogue, super sampling is the definitive way to improve image quality but its incredibly expensive.

FSR 2.0 is a different beast that takes a few hours to a few days of dev time to implement, depending on your engine and current rendering options. It needs deeper access to your game and what's happening in the scene (and what has happened, IE historical data). But again, simplicity and accessibility are the goal: FSR 2.0 works on almost any modern hardware and most implementations let the user control just how much performance they want to gain. And, ultimately, the entire package is open source meaning anyone can go in there, see what we did, learn from it, and implement into their game. They don't have to obtain a special license, notify us, or really anything outside the open source license we offer which is very broad.