I once sat on a committee at a university which examined this issue. The university had no explicit policy against professors dating students. We recommended that none be enacted. This was based on a few factors.
First, there was no evidence that this problem was common. There had only been a handful of reported incidents over a couple decades.
Second, there were already university policies concerning conflicts of interest and abuse of power which in the opinion of the university attorney were sufficiently broad to cover these situations. That opinion was supported by the previously reported incidents which used the already-existing provisions to punish wayward professors where punishment was deemed appropriate.
Third, some administrators wanted a uniform policy across the campus while others wanted different policies for undergraduates and graduates. This disagreement got heated and our committee did not want to get in the middle. So we did what all administrators do in that situation: we took the path of least resistance.
In our early discussions about the policy, the one issue that kept coming up was the age difference and relatedly, the maturity and social status of the student. In a typical undergraduate class, the professor is usually substantially older than the undergraduates with more maturity and social status. In a graduate class, it was not uncommon to have students as old or older than the professors with substantial careers already started. In my discipline, it was not uncommon for someone to graduate, work for a few years earning a high salary and respected credentials, and then come back for a graduate degree. In such a situation, the power imbalance is much less because the social statuses are much more equal and the maturity level of the student much higher. I can think of half a dozen professors who met their spouses when the spouse was a student in their class. In none of those cases, did it appear anything improper was being undertaken.
None of that affected me personally - Mrs. CommerceComet has a much more stringent policy on this than any university but she only has jurisdiction over one professor.
For clarification, in all the cases that I am personally aware of, the professors who met their spouses while the spouse was a student, the classes were all graduate classes and the students graduate students.
Social status and age are really secondary—I would argue even irrelevant. The real issues are power, integrity, and fairness.
If a professor is involved with a student in their class, there is always the issue of quid-pro-quo. That is: is sex being offered in exchange for something. Whether that is the case or not, that perception almost always shared by other students and the rest of the faculty. Even if the student is not in the Professor’s class, the Professor may have influence on campus that could help (or hurt) the student. I think the argument could certainly be made that they should not date any graduate student in their course and/or their Department’s degree program.
I do know of several professors who married students after they finished school....one very soon after. Trust me, it does cause a stir.