Valves initial support for linux was for precisely these reasons. Microsoft was talking about restricting which games could run on windows in much the same way an Apple does with iPhone software. The prospect of Microsoft having veto/censorship powers over violent video games struck fear across the industry. Valve then pushed towards "steam machines" running not-windows. Those issues have reduced as of late but were the trigger for what would eventually become the proton project.
I doubt that this is generally true based off the discussions I've seen in the Steam forums for various games.
So you're right, it isn't generally true today.
I personally don't use the Linux builds if the Windows version works with Proton, but I do download them for archival. I also don't submit bug reports to devs for Steamplay issues, so that's another factor.
The two goals that actually needed to be achieved were preventing market monopolies and enabling smaller devs, which platform agnosticism has been a welcome and necessary side effect of.
i) Reducing the resource overhead required to publish and support games is make or break for indie/small devs. Just by being Steamplay/Proton aware, compatible games don't require exclusive support, allowing devs to focus on content and expansion instead of learning quirks of all different distro just to be able to support that one user on Hannah Montana Linux. Helping individual customers feels great, but it can become a deadly rabbit hole.
ii) The market aligned against publishing monopolies, which Valve isn't singlehandedly responsible for but has been a major contributor to. Linux native was just a way to get devs and publishers to realize that they couldn't and shouldn't fall prey to the exclusive marketplaces on the rise at the time like GWFL that would only reduce choice and availability for customers and non-AAA devs in the long-term. Breaking OS dependence was key in this.
I think we ultimately want Linux to be able to do whatever we want, be that running video games, powering Mars rovers, or running our HPC clusters. Once software can be run with the same ease on Linux as on Windows, it might as well be Linux native, and non-FOSS Linux purist arguments are confusing and dilute that.