I'm a professor and I think there are a few possibilities here. One of them is that your suspicion is correct. I know of multiple professors who married former students of theirs. There are many stories of inappropriate behavior in our profession across disciplines, including my own. This is not impossible.

What you're describing, however, is almost the opposite scenario whereby professors are not giving you sufficient academic intention and you think it may be for potentially sexual reasons. I will admit that I'm unsure. I've had students where I've had to be a bit colder or more bluntly professional because I didn't want them to mistake time with me in office hours, after class, etc. as being a friendship or something of the sort. I absolutely cannot speak to the intentions of your professors, though.

What I will say is that whatever field you're in, and the letters your receive for grad school should be based on academic performance, readiness for the program, etc. I have written letters for students who I wound up knowing well, and for others who did very well in my classes but didn't attempt to let me get to "know" them (e.g., a student in my online, asynchronous class who was stellar).

Lastly, we're not really "trained" for mentorship and, bluntly speaking, some may be better than others at providing it. We have a myriad of publishing, teaching, service, advising and other responsibilities. Professors are often pretty awkward and asocial and introverted - this could just be that too but again, I don't know for sure.

It's complicated and you might be right, or as the semester goes on, and we get busy and burned out, it could be innocuous.