Lots would depend on the kid. My engineering grad had a GPA >3.8, but would have been very uncomfortable and possibly stressed to the point of being dysfunctional, had the major required this for entrance. This would possibly be true of several classmates with similar GPA’s.
I would be wary of any program with competitive admissions to a major, or a “winner take all” weeding process, especially if there is no attractive back-up major.