Having police for demographics seems inherently suspicious from a standpoint of liberty as it is either for undue crackdowns or undue lenience separate from official legal status. To give an absurd yet rationally based hypothetical - if it was official that it was in the interest of the state and people for college students to get more lenient drug and alcohol sentences because they want to encourage a limited degree of exploration to better innovation they wouldn't need a seperate police force because it was already codified in law.
This is distinct from when there are actual practical differences for given groups to be policed - a specialized white collar crime police force makes perfect sense as the needs are different. Similarly military police in a provost [https://en.wikipedia.org/wiki/Provost_(military_police)] role are justifiable.
I'm not saying campuses should go unpoliced. I'm saying that the approach is suspect for the situation even if it is just a stupid historical artifact. Keeping an office of a police station on a sufficiently large campus but part of the normal state or city policing is fine - just because they are part of a university doesn't mean they are outside their jurisdiction. Deciding to have a security force that specifically don't have policing powers but enforce rules 'privately' is also fine.
2. Universities have often been actively hostile towards various groups
These two facts caused a lot of government regulation to be applied to universities, which includes the university taking steps to prevent a "hostile environment." This means that policing harassment is often a legal requirement on universities, and was put in place so that the universities could not rely on the existing student body to do the discrimination on behalf of the university.
That is to say prior to the laws that are being applied in this case, we had laws against harassment and they didn't work. At least partly this is because harassment is usually not a federal crime, so the federal government could not force the states to enforce those laws.
Universities are not equipped to investigate and have guidelines to do so with due process. Making them responsible completely bypasses entire sections of law.
Somebody threatens you at the gym. It's not the gyms responsibility to investigate and take action. You call the cops. That is what you do.
Making other organizations reposnable for legal matters is just a way to bypass the law and do whatever the hell you want.
Simply put universities can't be the judge jury and executioner of the law.