It's a collaborative effort. The Wine and Vulkan projects have all done a lot and deserved credit for doing massive, amazing things. But for Linux gaming specifically, Proton has absolutely changed the landscape, and if Valve continues down this path, will make Linux an ever better gaming platform. So I don't think it's unfair to say thanks to Valve.
Not only have they sunk significant resource into making Linux gaming more viable, they've released Proton under BSD and seriously pushed developers to make Linux-compatible binaries. If Linux continues it's slow upward trend in popularity, Valve will be in large part to thank.
The cost of administrating benefits, ie fact checking and means testing and complex rules etc, typically costs 1-2x as much as the benefits themselves. It's not even about saving money, it's about making sure that poor people are sufficiently screwed.