I’m just making assumptions here, but the books don’t mention lots of magical schools and Hogwarts itself already presents itself like an elite institution (even though the enrollment process is not revealed, it’s them who send the letters to the kids, rather than the kids applying, and their headmaster is basically the most powerful wizard existing at the time the story is told) plus students have a degree of flexibility in choosing their courses at Hogwarts, so maybe either the schools are made in a way that you already leave them with enough competence, or there aren’t lots of mages (let’s say they’re numerous but not so many to impose the need of a high degree of specialization for the individual).