I'm going to offer an alternative.
Steam lets you streamplay games from your computer to another computer.
Your phone is a computer.
You don't like the built in controls for a phone.
You can pair xbox and ps5 controllers to androids phones with little to no effort. Not sure about other phone OS's, and quite frankly, not my bag baby.
So now you have a controller hooked up to your phone, and it's channeling games from your computer over wifi.
Never had a cause to try it personally, but I might just do that and come back to confirm it works.
Might save you a couple bucks for your kids college fund.