At the end of the day, it doesn't matter where you move compilation to, even if you could move it..
The main problem we currently have are developers not properly implementing complete compilation/caching systems into their games. There's also a problem with Quality Assurance, and developers/publishers releasing games in these kinds of states. You can't play Ghostrunner, or Shadow Warrior 3, or many other games for even 3 minutes without seeing very CLEAR problems here. Unreal Engine 4 games are notorious for this. Same with FF7R for crying out loud. People tested these games... and apparently it was acceptable for them. THAT is a problem.
I can understand some small indie dev team with no real low level programmers having issues... but SquareEnix?
Are developers and game testers properly testing games... which clean shader caches? Do developers actually play and test these games after they hit the final "build"?? Because in my mind, a developer would build the game, and constantly be testing how levels perform, by constantly clearing the caches. If you don't do that while you're testing... you're not getting the same experience that gamers will get when they first experience the game.. and the testing is useless.
Capcom seems to be one of the ones who does it right. I don't remember any compilation stutter in any of their RE engine games utilizing DX12. These games don't have long shader compilation processes at the beginning either. Monster Hunter Rise actually has a small shader comp process at the start to ensure it's all precompiled.
GPUOpen presentation by Capcom and AMD about DX12 optimizations in RE Engine
https://gpuopen.com/gdc-presentations/2019/gdc-2019-s4-optimization-techniques-re2-dmc5.pdf
Basically.. we need more developers to just start putting more of a focus on fixing and optimizing this aspect. If engine providers can improve how developers can capture the required data to build better pipeline caching systems.. then they should immediately begin implementing it.
We have the CPUs... we have the ability to pre-compile on our end.. We're willing to wait for these processes.. We just need them to be implemented.