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.
A prohibition on professors dating undergraduates is a clear call in almost everyone's mind. It seems to be prima facie abuse of power.
It is not so clear that a professor dating a graduate student is taking advantage of the situation.
You raise some valid concerns about the perception of integrity and fairness. In the discussions I referenced, no one ever suggested that a professor dating a graduate student was a good state of affairs. The question was should it be tolerated.
The three marriages that I am most familiar with between a professor and a graduate student didn't raise a lot fuss. This is probably due to the fact that each took precautions to avoid appearances of favoritism. All three marriages have lasted, one for almost 35 years now.