Only the first port (Tomb Raider 2013) had performance issues wich can be fixed with a few tricks, nothing that you can´t do or GOG can´t fix.
Don´t believe me? Try it, just use "mesa_glthread=true %command%" if you have an AMD graphics card, or "__GL_SHADER_DISK_CACHE_SIZE=4000000000 __GL_THREADED_OPTIMIZATIONS=1 %command%" if you are using an Nvidia GPU, those commands will help a lot.

Now, if we talk about the ports of Rise and Shadow, those are pretty good, and don´t have the level of stuttering and perfomance issues that the first port had, and you can enhance the performance also with commands, again, nothing that GOG can´t fix to get the best experience.

Finally, the Linux port of Tomb Raider 2013 was pulled by Feral because the licence of the port expired, Feral knowing that Proton was slowly becoming the best way to play games on Linux, and looking that the Windows version ran better than the native one (because of the way that the port was made), they for some reason decided that the best choise was to not renew that license since it wasn´t even worth it to try to make the port better because of Proton, if that was a good or a bad choise, there's no way to know, but what i do know is that those ports are part of the history of PC gaming, and the problems that they had can be fixed or at least mitigated with patches that GOG can perfeclty implement, so there's no excuse.

Use Heroic Launcher on linux and you can play these games fine.

Since I have the three latest Tomb Raider games in native version on Steam, I had also added those games to my wishlist here, waiting for a good deal (I'm rebuilding my library with DRM-free games, a good idea especially seeing the stupid laws that are starting to come from the United States and the United Kingdom), but as soon as I saw they didn't have a native version, I removed them.

There are already so many native games that it's not worth wasting time and money on ones that don't have it. Indies, which paradoxically manage to maintain native versions despite having smaller budgets, can afford to do so. Forget about big companies and their AAA titles, indies will give you thousands of hours of native gaming fun for a fraction of the price of a big game that only lasts 10 or 15 hours.

And if, for whatever reason, the native version stopped working you'd have the non-native version as a backup. Double the options. For the game to become non-functional both versions would have to fail.