It creates confusion.
It forces BYU-Idaho to constantly live in the shadow of BYU. It has created the "BYU, but for kids not smart enough to get to wear shorts" sort of second class feeling.
The fact that BYU-Idaho has no mascot, a borrowed named, zero research profile, no school colors......What are BYU-Idaho students supposed to rally around? They're just this amorphous blob of an overflow. What is their identity? ("BYU is the academic school, BYU-Idaho is the more religious school"-former BYU-Idaho girl in my ward).