I've distributed the info about Special:ClaimMentee to Czech instructors, and they did want to be a mentor for their own students, but not a general one, because they're afraid it's a lot of work.
Let's allow anyone to claim a mentee for now. It's not a widely propagated feature, and in the unlikely event of abuse, it's possible to prevent claiming by blocking. If that happens, it's easy to introduce claimmentee right and assign to autoconfirmed (or whatever we want to).