I think student-teacher relationships are interesting and very readable. It doesn't matter if the age gap is large or not, or whether it's female student or male student. As long as it's plotted like any other romance - with plenty of conflict - it's readable.
And yeah, it is very common. I remember reading Goodreads reviews for TEACH ME and was amazed and how many girls posted reviews along the lines of, "This isn't anything like how my affair with my English teacher went, or how my friend's relationship went either!"
When I was 16-18, most of my teachers were young guys (21-23) and yeah, it was obvious if they liked certain students. But they did their very best to stay professional, even if it was strained at times. To my knowledge they never did anything, and there were plenty of girls who liked them.
There's much more scope for 'casual' student-teacher friendships over here though. Post-16, students call teachers by their first names and everything's much more mature and friendly. One of my teachers (21) even told me where he lived and which pub he went to each night. He was just being friendly (and grossly unprofessional). I never met him outside school, but plenty of others did. And I doubt he intended anything because he was happy with his girlfriend. (And the drinking age is 18 here, so you could theroetically go drinking with them. And, some did.)
Of course, the US system, with last names and internal grading, and there's more conflict from these angles.
That said, younger than 16, and any kind of flirting is just noticeable and cringeworthy. I had young female teachers in secondary school (11-16) and it's obvious they liked some of the 15- to 16-year old guys. I also saw an instance of a male teacher flirting with a 15-year-old student for an entire lesson.
And, wow, don't I sound like I went to school with a bunch of unethical teachers?
Also, as well, as per the title of your post, avoid cliches with this type of romance. I've seen really typical scenes which are just bad writing, such as teacher gives student he likes detention - or student deliberate gets detention to spend time with teacher. Student visits teacher at lunch time to help out with things, or does this after school. Student stalks teacher's car and follows it home and finds where he lives. Student investigates teacher online and uncovers past.
It's difficult to build a romance when there's such a barrier up between the protagonists, but I see the above happening repeatedly. Although, I did see a female teacher deliberately giving detentions to the good-looking male students who she seemed infactuated with. They also seemed pretty happy and even got their diaries out to arrange the most convenient date! So hey, maybe it happens a lot.