BYU-I, Utah public schools nor any other public school, the service academies excepted and they--USNA particularly--are as selective as the Ivies, a much more difficult application process than BYU.
I do believe the BYU experience to be beneficial. The solution, in my view, would be for the Church to start even younger--grade school and high school--using the chapels that are vacant all week, and then feed those into a series of regional "BYUs."
That would do more good than the present YM/YW programs and they could be eliminated entirely.