It’d be dumb not to learn everything Tsunade has to offer.
Are you really going to accept that Sakura of all people is more skilled and talented than you?
I think making him become Tsunade's apprentice isn't that bad, in fact I think he could become much stronger since Tsunade is super unlucky, and therefore he could learn more skills.
Tsunade is like the perfect mentor for mc? Don't forget she has godly genetic and like to bet
Learning only medical jutsu isn't advisable but not learning any? That's dumb as hell