You're effectively saying non-permanent residents should be prohibited from using commercial flight to move around the giant country that is the US. I'm not sure if that's your intention.
I've personally flown domestic commercial flights in at least two foreign countries (China and Mexico), that I have no legal permanent residency in, using the same American passport I used as ID to enter these countries to begin with; and there was no issue. I don't even know what the Chinese or Mexican equivalent of a REAL ID might be like. I'm sure the US could create a similar legal ID framework for domestic air travel.