Heck, if we had a mini quest in Avernus related to Karlach - house of hope could have been a good start but nooo, once again related to Lae'zel's questline! We could find ways to fight for her heart, meeting Zariel, her giving her some sort of ultimatum or something (some kind of a trade off much like with Shadowheart).
But no, we don't even try. The game literally doesn't allow us to try.
