If you don't use dedicated hardware then you have to use general hardware that is used for everything else, everything else then slows down as a result due to the greater workload on that general hardware. I'm sure AMD only took the route they did due to budget restrictions on creating a console chip, RDNA2.
I already said there is another trade off. Take for example a console like X box X. What do you put inside the chip? Do you put more compute units that help rendering in every game or do you put specialized cores that are only used for upscaling/denoising, especially since 99% of games don't need upscaling or denoising and you can do the same maths the specialized cores are doing, on shader cores with some performance impact?
Once DirectML becomes a standard and it will be implemented in future games, the Xbox X will be able to run any game at upscaled 4k-60FPS without any specialized cores. So that part of the chip is almost useless and it can't do anything else.
Dedicated hardware is a thing for Nvidia because they can use it right now to get a huge advantage over AMD and to force older Nvidia cards to become obsolete. But for such tactics, you need a big team and a big wallet, to pay the developers to give you access to their code and to put your code inside their games.
Because on PC it matters if you get 80 FPS instead of 100, even if both results are obtained at a fake resolution, AMD will probably use dedicated hardware in their next generation knowing or hoping that directML becomes a standard and that way they can compete with Nvidia. Without a standard they won't be able to compete as they don't have the manpower or the money to support their own proprietary technology.
I am sure Nvidia is not happy either because they have to spend a lot of resources for every game that gets RT and/or DLSS and that is why is trying to push the narrative and hope the developers will use their own money to add RT and/or DLSS support in their games. But at least Nvidia is using their proprietary tech as a marketing tool and they are doing a good job at it so these are money well spend. And i am sure that once they lose the advantage in upscaling/denoising, they will focus on something else and promote that thing.
What i want to say is that none of these companies are stupid. There are reasons for why Nvidia has dedicated hardware (marketing) and there are reasons for why AMD does not have it atm(lack of resources and no standard). There is a reason for why Microsoft and Sony don't use it in consoles either. They simply won't need it for their future upscaling plans.