This has been my experience. Ubuntu "just works". What would get better with what you propose? (speaking from ignorance)
The other key benefit would be driver management. Updating your drivers right now can be a nightmare. If the drivers are open sourced and upstreamed into the kernel this becomes a non-issue. I do understand why Nvidia doesn't want to do that though. A lot of their lead right now is not just hardware based, but software based. They have a choke-hold on the ML ecosystem and it's a huge cash cow for them. Giving away that secret sauce in their drivers, so that AMD could make their cards seamlessly compatible would probably be a huge mistake from a business perspective for Nvidia.
I've seen this argument a lot but never from the ML perspective - and I don't think it makes sense with ML.
Nivida's advantage is ML is CUDA and cuDNN, and the huge set of tools built on them. These aren't the driver, but a layer above it.
I don't really understand the "secret sauce" argument for the drivers at all, but I assumed it applied to gaming somehow. I can't think of how it applies to ML though.
Intel and AMD despite their FOSS support, actually only do open what they feel like.
(Nvidia cards have two drivers on Linux, nouveau, the open-source, slow, and incompatible-with-Quadro ones, and NV, the binary blob shipped by Nvidia that people take religious exception to.)