Mobile is far and away the most profitable, highest revenue segment of the gaming market by a huge margin. I can't imagine they don't want a piece of that.
Valve released a phenomonal but imperfect update to the Nintendo Switch which has sold about 1% as well. If Sony released a PlayStation Phone tomorrow, and failed to update it for years despite massive interest, then you'd see a SteamPhone.
* strong, like STRONG competition from global leaders a la Apple and Samsung
* much deeper requirements for OEM builds, otherwise they're just white labelling hardware. makes sense for the Steam Deck since the offering is the Steam software and compatibility layer.
* they're in the business of software and software support, and some light hardware support viz. the Valve Index and Steam Deck. but the average person looks at their phone 5+ hours a day and defines many of their life functions are dictated by their phone -- e.g. alarm clock, fitness tracker, music, many forms of interpersonal communication. they will drastically need to up their QA, support, and compatibility -- and those have non-trivial costs.
* OEM manufacturing has ruthless margins; they're a private org but still
* non-trivial build and launch costs
If only Valve had a world class digital marketplace...
The point is that they have one now. SteamOS is 10 years old at this point. They've undoubtedly dumped millions into it already, and done most of the wireless networking, battery performance, and UI work needed for Steam Deck. It's a pretty short leap for a company like Valve to add a 5G modem and miniaturize the form factor from there.
It's hard to get around the awkwardness of the physical button problem though: having buttons makes the phone awkward, not having them makes gaming awkward.