How many would buy a gaming-first phone (by Valve)? I don't quite know what such a product would mean in practice, or if there is a killer "app" (game) for phone. But it would have higher probabilities of success than "a real Linux phone".

Gaming oriented phones exist for sure. One by Valve with SteamOS, yeah maybe.

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.