The purpose is to take education to the masses and give many kids a chance they would not have previously had.
With that being said, alumni connection and involvement is reduced significantly. I know that my parents and grandparents, being Ricks grads, do not donate to BYU-Idaho. It's a different school in their minds. (I think that Thomas Ricks being my great great great grandfather also has something to do with it. My family was not thrilled with the name change. It's a bit like the Dairy Yewts taking Merlin Olsen's name off the stadium).