I think this is a really interesting topic.
As a patient, I have developed at least a partial erection every time I get a genital or rectal exam from a female, and it's even happened a few times when being examined by males. From my experience as a patient, they are very common.
However, I am also a physician. I have done thousands of genital exams on males. Most of these have been adults, but I have done some teens and children as well. Many of them were ill. Nevertheless, even when doing sports medicine 'production line' physicals with high school boys and with female chaperones in the room, I probably don't average seeing more than 2 patients per year with erections during the exam (as long as you don't count priapism, which is something else entirely).
So - a weird disconnect -- I get erections very easily as a patient, but see them quite infrequently as a doctor.