Hearing petitions is a pretty standard part of Westerosi royal tradition. It was unwise to conquer Meereen in the first place, and more unwise still to stay, but I don't buy that it's stupid of Daenerys to govern the city herself, especially since (some of) the people love her
, not her functionaries, and since the pool of possible individuals she might delegate to
is limited. That, I think, is a large part of the problem with Daenerys: she doesn't have any knowledgeable advisers she can be guided by and entrust things to. Barristan is noble and loyal, but he's hardly a political genius, and a lifetime in the institution of the Kingsguard has made him too deferential, especially when faced with a highly confident monarch like Daenerys. That's what Tyrion could be good for, if he ever gets to Daenerys and she's able to recognize his skill: he has the intelligence and the cheek necessary to get through to her.
If Genna had actually being telling Jaime something about his biological parentage, it would be a bombshell. But that's pretty evidently not how she meant it.