They are exceptions, but the exceptions happen fairly often. Even Rodgers fell to pick #24. The Saints could have drafted him but took Jamal Brown at #13. Dak was a 3rd or 4th round pick. Brees was a second round pick.
Mickey certainly takes the lion's share of the blame for not drafting QBs, but part of it I'm sure was that while Payton was here he always wanted to improve other areas of the team for a shot at another SB rather than take a developmental QB. Then the year Payton ID'd Mahomes, he told Reid how good he was and KC traded ahead of us instead of us trading up to get him. So, some of the blame falls on Payton, but that's Loomis' biggest flaw, he won't tell his HCs no and he doesn't force them to use draft picks for the future of the team beyond that particular HC.
Word from Underhill is that Ireland is actually very good at evaluating QBs. Apparently he has always pretty much so been right on with his evaluation of the QBs in the draft, especially the upper level guys, but the Saints just don't draft them. And, yes, that's on Loomis.