It only takes 3 exceptional players, 3 solid role players, and 3-5 decent bench players to be a national powerhouse in basketball. Football requires a much higher number of exceptional players to be elite.
It’s also much easier to recruit 3 exceptional players to play in a mid tier basketball league than it is to recruit several exceptional players to play for a non P5 football program. Look at what Gonzaga, Wichita State, and others have done with their basketball programs.
I know we all love football and it’s baked into BYU’s DNA to think of ourselves as a football school, but the reality is that BYU’s potential to be a powerhouse program and household name is much higher with basketball. Personally I wouldn’t mind being known as an elite basketball school.