Ideas like this haven't come up for the first time. I expect this idea occurred to Valve and they thought it was not worth the investment of money/manpower/infrastructure.

Valve would either have to publish on Google Play. That would put it in the role of a developer and Valve is not really pushing on its developer role significantly. A huge cut off sales then goes to google.

Or Valve will have to try to make an alternative store.... And that is no small feat. Most people will not sideload apps or install other store fronts. I imagine the proportion of android game sales that Valve can get into will be tiny enthusiast communities, and that won't be anywhere near enough to pay the bills. On this alternative store, Valve will have to get developers to make games.....or again they will have to consider developing games in house to get the ball rolling. Their best bet would likely be to use their existing IP to make mobile spin-offs (DotA card game? Or a wild-rift type MOBA? CS:GO turn based tacticle game? Or try to compete with CoD for the FPS market?).

I can't see any combination of the above that seem like probable success for Valve. It's admirable that they're sticking to their niche and what they know. Pushing further into the handheld gaming and console market has been a much better option for them and they're trying hard. Even in that aspect, the Steam Deck is universally praised......and is selling roughly 2.5% as many consoles as the Nintendo Switch. And no one I know IRL knows about the Steam Deck (other than my brothers, who bought one after I told them I had pre-ordered mine).