Phones with buttons have been tried and failed. Same with using your phone's processor for a desktop environment by simply plugging it into a dock; Samsung's DeX comes closest, but very few people seem to use it.
In practice, the easiest way to combine phones and games is to either stick with the touch screen interaction all games are designed for, or to grab a Bluetooth controller. Works across many games, almost all phones, and you have a pick in the hand feel or button quality rather than being limited by the design choices of the phone designer.
If you're into playing games on the go, tools like the Steam Deck or one of the more recent cloud streaming handhelds are probably better.
A few years ago my building's elevators were breaking down and had to be completely replaced. The new ones have a touchscreen that only ever displays the floor numbers, and real buttons that only go up to 9 (in a grid like a phone) where you have to hit two of them to go to floors 10+.
Check every elevator carefully, ADA regulations sometimes require at least ONE elevator in the building to have real buttons (for the blind, for example).
A hotel I stayed at had touchscreen "requests" for elevators (you put in your floor and it would call a elevator for you) and it was super annoying (trying to get floor 12 would doublebounce on 1 and 2 so you'd often get 11 and 22 before getting 12) until I found a pedestal out of the way that had real buttons for all floors.
The "hold your keycard up against the thing" is also really annoying when it is 5 feet off the ground; imaging having to wait for an elevator until someone comes along who can hold your card up there for you.
Sounds like that can easily be fixed with enter and backspace buttons.