Let’s be honest, any decent mage took part in BFA, so that being a disqualifier for the open post is going to severely limit the pool.
To put it another way, would you rather have Jaina, or Umbric on the Council of Six, if you had to pick one or the other?
For all Umbric did, he paid heavy lip service to, “it could be worse,” and, “we’re being super responsible and not letting it get out of hand because we know the consequences. This is a controlled ritual.”
If the Void is actively becoming a threat, I think Khadgar would be interested in finding an expert to join the ranks. I think what would be the weirdest part of Umbric joining the Council of Six, is that we have no lore suggesting he was ever involved with Dalaran. Of course, he’s so underdeveloped as a character that Blizzard could just say, “Oh, Umbric was a high ranking member of the Kirin Tor for millennia before he went back to Quel’Thalas,” or something.