I think you are correct that the major goal of BYU was to provide a good education for a whole lot of LDS kids. It wasn't necessarily meant to provide anything more than something analogous to an state-school-level education, but in an LDS environment.
But its evolving into more of what you'd expect an "elite" private university to be. Don't get me wrong - its no Stanford, not by a long shot. But the progression is in that direction.
BYU-I now provides an environment and education consistent with the earlier goals of BYU.