It would make sense, but the question remains of how to do it. Also, whether characteristics like Com and Pre are fully "developed" in childhood - some quiet children grow up to be quite dynamic, and some of the more outspoken never develop anything more than a loud voice. Likewise some Virtues - how does one spot Puissant Teacher before a child learns to Teach? It (perhaps) can be done, but some SG's/Troupes might not be interested in the process - but it's another potential side-thread for any who want to make it such.
(Imo, any such benefit is always more appreciated if it takes in-game effort to achieve it, but every troupe differs in what it finds "fun", and that's the most important consideration.)
Once found, there's always the problem of acquiring the (prospective) tutor - unlike some trades, an uncooperative, unwilling or uncomfortable target would hardly make the best candidate, tho' there are always magical ways around any such obstacle. The prospect of working daily around The Gift would not make for the most attractive work environment.
Speaking of which, I guess it's never too often to trot this old pony out:
http://www.io.com/~sjohn/demog.htm
The author has put together an "average" population requirement for supporting the most common/necessary medieval/fantasy world occupations, and includes many that one often does not think of. All this is averaged from "medieval Europe", and, of course, is not reliably accurate for any one locale or time period - but it's better than faking it if you want to be close to historical accuracy.
If you aren't of a mind to read the "whole" page (it's good, do it!), the chart in the middle shows the SV - "Support Value" - for any trade. That many citizens will support 1 of that trade, and if the town/village/burg/hamlet has less, then that can be used to calculate the % chance for that Trade to be represented; if more, that shows the chance for more than one. A separate paragraph below that deals with "institutions of higher learning".
Bottom line, that research implies that tutors would be rare as hens teeth.