Squiddy, it would help if you'd stop thinking of them as "cock doctors". Seriously. A urologist's responsibilities include the whole apparatus, not just the penis. Kidneys, bladder, prostate, ureters, other parts as appropriate and every disease or condition that affects them and vice versa.
A layperson's first reaction to a lot of medical things is "Ewww, that's a butthole! Shit comes out of it," or in this case "Touching cocks is, like
so gay." That's really where your whole question comes from. That's why I made the remark about ugly slimy things that live in the ocean. It's an outsider's question that someone who has already made the decision to study biology wouldn't think of asking. After you've seen a few thousand sets of lungs or genitals or spleens they lose their mystery emotional associations.
Someone who is already in medicine and has gotten beyond that sort of thinking has different concerns. It might be an intellectual interest as pure as what drives one person to invertebrate zoology and another to something more interesting and worthwhile like gauge theory

It could be an influential experience with a particularly good professor, the dictates of the marketplace or the emotional and personal satisfaction mentioned earlier.
"It is the difference between the unknown and the unknowable, between science and fantasy - it is a matter of essence. The four points of the compass be logic, knowledge, wisdom and the unknown. Some do bow in that final direction. Others advance upon it. To bow before the one is to lose sight of the three. I may submit to the unknown, but never to the unknowable. The man who bows in that final direction is either a saint or a fool. I have no use for either."
-- Roger Zelazny Lord of Light