Because the muggle parents either aren’t narcs and just keep the secret like they’re supposed to, or if they really just can’t handle it and insist on being douchebags their memories are modified so the statute of security isn't breached.

No qualifications? They’re all clearly experts in their field, obviously with the exception of Trelawny who was brought there and kept there to be protected from Voldemort. McGonagall is highly skilled at transfiguration, Flitwik at charms, Snape at potions, etc. Riddle is turned away by Dippet specifically because he…

When the students are picking out their N.E.W.T. classes (beginning of book 6 I think?) McGonagall advises them on different career paths and specifies to Harry that Aurors have a pretty hefty amount of rigorous schooling and training after Hogwarts. Being an Auror is portrayed as one of the toughest career paths for…