A lot of older PC games can run just fine on modern phone hardware. I’d buy a SteamOS version of a phone that has some modular or built-in set of buttons and analog sticks. I don’t know how the app ecosystem would work for sensitive things like banking but it’s mostly a minor issue for me.
I just made a similar comment and totally agree on both points. In the past, handhelds were actually this small, like a (bigger) phone with controls attached. Smartphones have bad battery life too and if its based on Android, then privacy concerns too. A dedicated handheld should be cheaper then full fledged power smartphone being able to play those games.