Gentoo is source based, and while distribution of binary packages is possible with it, why would they do that?
NixOs ignores FHS, and while it is possible to install a steam compatible runtime, why would they do that?
And Fedora belongs to RedHat, and why would they do that, when they actually try to switch away from a OS distribution controlled by one company?
I am not saying those distributions aren't good, just that it would not make sense for Valve to use any of those.
Debian (via Ubuntu) and Arch are probably the most well tested Linux distributions by gamers, that do not belong to a single company.