I think the pick for Arch makes a lot of sense if you consider the big players in the ecosystem:
* Debian habitually ships ancient versions of software unless you setup backports. It's also by far the distro that makes the most downstream modifications to software, which causes issues with upstream.
* Ubuntu is a semi-rolling (basically, a stable copy every 9 months) release of Debian + Backports with a Canonical skin and nice branding. Cute, but it inherits the same problems that Debian has.
* Fedora is fine, but it's also very beholden to Red Hat. Whilst Red Hat going IBM squeeze mode occurred after Valve picked a distro, the ties it has to Red Hat are a problem for Valve, considering their Linux push was always defined by not wanting to be tied as heavily to a third-party vendor (it almost entirely originates from Microsoft blowing their left foot off with Windows 8 and the Microsoft Store being both awful and a direct competitor to Valve; Gabe Newell is an ex-Microsoft employee, he probably recognized the direction MS is going in). Also, major system upgrades with Fedora aren't exactly the greatest process; they work, but since they're inheriting the CentOS structure, Fedora isn't really build around that sort of thing. I've always had to do manual checkups on key software when using Fedora.
By contrast Arch has a policy to "ship as close to upstream as possible" (even in cases where it's weird; last I checked, their nano still has the bad word wrap that nano is known for), pushes out updates extremely quickly and is a non-profit. With Valve having their own button on the upgrade process, they can also ensure that you don't get some of the more typical "hilarity" of running Syu and realizing your drivers made it so you ended up in an emergency shell mode.
Other distros just don't have the installbase to guarantee consistent support (everything on distrowatch) or are too inaccessible for regular users (aka "why not NixOS" -> because NixOS actively requires you to ignore almost every online resource and to only use the NixOS provided documentation since nothing else on the planet works the way NixOS does. Gentoo also is in this category, since most people that own a Steam Deck probably aren't looking to custom compile everything.)