There are tons of Linux games distributed on GOG, and not having to use a proprietary client is one of its great advantages. Not to downplay Valve's contributions (and I may well get a Steam Frame when they come out), but they mostly amount to porting their mandatory DRM-laden client to Linux, and maintaining a fork of Wine that integrates with that client.
Ownership, control, and privacy are among the main reasons I use Linux, and are likewise huge advantages that GOG has over Steam.
You're fairly significantly downplaying their contributions. They have a substantial amount of FOSS developers under contract working on SDL, DXVK, VKD3D and there's over a dozen people on working on KDE on Valve's dime alone. Proton isn't a fork of Wine, it's a Codeweavers managed project funded by Valve that packages Wine, virtually everything useful ends up going upstream given Codeweavers are also the main contributors to Wine. AMDGPU, NVK, Valve funded. Valve have been funding FEX since it's conception.
That isn't even everything, just what I've been able to confirm either through interviews or conference talks where their involvement has come up. They've quietly been doing a lot for Linux.
Official Linux releases are almost never maintained. I have the same game on Steam and GOG, but the GOG version no longer works. Neither does the Steam version, except if I switch to the Windows version with Proton. Then it works flawlessly (usually faster and better than the Linux version ever did.)
Can you give me an example of what you're referring to? I've got a lot of Linux games from GOG and have never encountered any situation in which the Linux build stopped working, nor any situation in which the Windows build was being updated with new versions without the Linux build also being updated at the same time.
Sadly I've had the same experience. I've had to rebuy a couple games on steam because the older gog version wasn't version compatible with my friend's clients. That really burned my bottom.
Yes, it is so bad that I will no longer buy a game for its Linux release. Almost every single Linux game I have outside of actual Valve titles no longer works. I don't want to hear that they have a Linux release. I want to hear that they have a Windows release that works with Proton. Windows is the only ABI that I can expect to reliably run on Linux.
I've been gaming primarily on Linux for almost 15 years, and buying from GOG as my first choice, and have never encountered a single instance of what you're describing. I don't have a single Linux game on my GOG account that "no longer works", and I have dozens of Linux games there.
In fact the only time I recall a Linux-native game not working out of the box was when I got the game 'The Raven: Legacy of a Master Thief' on Steam, and that was due to some wonky configuration implemented by the game devs.
Do you have any specific examples of this problem?
Ownership, control, and privacy are among the main reasons I use Linux, and are likewise huge advantages that GOG has over Steam.