NVIDIA literally couldn't make this work on AMD cards if they wanted to. The hardware simply does not exist on AMD cards to run it and so the performance impact on AMD cards would be worse than not using it at all. Then everyone would complain NVIDIA is purposefully crippling AMD.

Contrary to popular belief FSR isn't behind DLSS because NVIDIA has more magical AI capabilities to train DLSS, and AMD through partners like Microsoft and Sony have access to just as much if not more AI training capability to train FSR if they wanted.

Additionally, NVIDIA isn't going to be wasting any more AI horsepower on training DLSS than they have to when there is essentially infinite demand for it from high paying customers right now. If training your algorithm was the secret sauce AMD could do it too, and they'd be able to catch up simply by spending more over a shorter period of time.

The problem is that FSR has to be extremely lightweight to run, because it competes with the graphics rendering for resources. The more AMD makes FSR do the less performance advantage it will provide. DLSS on the other hand uses the tensor cores that are otherwise unutilised on RTX cards. This means DLSS can be a significantly heavier and more complicated system because it has essentially free resources to run on.

Until AMD has standard tensor or some other free performance to use on their cards, FSR is going to remain behind.