There are myriad reasons, but trust me when I say that there was a rift at CU decades ago, and that was before many of these moves toward professionalism occurred. I think many of the traditional students would say they can do many things that the majority of the student athletes cannot, and what they can do is more in line with the underlying mission of the university than sports.
I do understand your point, though, and there is merit to the special skills argument, but the rift will grow if you are paying athletes a salary, NIL, scholarship, health insurance, and post eligibility benefits, all of which are on the table. At the same time, these students are facing escalating tuition costs, housing costs, student fees, health care, and so on.
I also disagree with the premise of no rift with professional sports and the public.
First, it’s an imperfect comparison because the professional teams like the NFL are operating privately within their stated mission (much different than universities).
Secondly, there is a rift between the public and, say, the NFL, as an example. The NFL has a huge fan base, willing to pay up, but it also has an equally large group that hates it at every level, and a large part of society in the middle that’s simply indifferent. The rifts tend to show up when certain flash points occur like public financing of stadiums for the benefit of private enterprise with dubious economic justification, very public criminal activity from the players, or player protests and advocacy. Sometimes I agree, and sometimes I don’t. But there is still a rift, and it is absolutely growing in professional sports. On a personal note, my wife absolutely hates the NFL, and laid into Watson case at dinner last night after his suspension was announced. She does not understand why he isn’t under criminal indictment.