This is why I have a separate Windows PC for gaming, that I do not ever put personal information into, or use even to sign into my personal, non-gaming accounts (e.g. Gmail). Perhaps not a good solution for everyone, but I think that's what the world has come to.
This is why I settled with a PS4 last year. Even on a Linux PC, I would feel "dirty" with games and steam installed, and I can't afford a PC exclusively for gaming. A PS4 costs 300€ and runs Skyrim, so I am quite happy. I am also speculating that the PS4 will become completely owned by the community and ultimately runs Linux without anything missing.
At one point I built a "Steam Box" that ran Windows (because, at the time anyway, lots of things didn't run on Linux), and hooked it up to the TV. The only problem I ran into was that lots of games don't do controllers well, either.
I have the same setup and controllers aren't really issue on modern games anymore - they're all released for consoles as well so they usually feature good controller support.
I did the same thing. It ended up being used mostly for watching streaming services instead of gaming for social reasons (the TV is in a shared area). I ended up buying an even bigger more powerful gaming PC with dedicated gaming keyboard and mouse and no controller. Linux for work, Windows for streaming TV, Windows for gaming.