Sony is not going to create a new solution for base PS5 when its almost 4 yrs into its lifecycle. The PS5 Pro is their answer for a better solution.
If you want better upscaling then sell your base PS5 and buy a Pro, not hard.
Eh, they could. There will always be more PS5 base-models out on the market than Pros. And especially if 3rd-party solution like FSR improved things on the existing box (especially an open-source solution like this,) then Sony should bring it to these versions of their games.
However, there's not significant indication from reports of using FSR 3.1 that AMD has reached a level where the existing solutions have run behind. So, it is what it is right now.
(Sony might not do it anyway, even if it did clearly improve things, because console patches are a pain in the neck for some reason to even first-party providers and Sony doesn't have the best rep of patching graphical functions to their games. But it'd be good if they did, if it was worth doing.)