BYU student doesn't come from a family living in poverty, but they don't come from a family that could afford a whole lot of tuition either. There's only so much money you can make in a part time job (which is about all most kids can do and get good grades at BYU). The rest would have to come from loans. Which would leave the average BYU grad with greater student loan debt. And, I don't think the church wants that.