I bet there will still be people complaining about that their character is from Yartar, or Waterdeep, or Neverwinter, or w/e other place they want ... but hey, cant satisfy everyone.
So either that ... or adding check box in character creation:
Owning a house in Baldur's Gate? Y/N
Y > Sory, it was confiscated ... but if you help us, we can do something about it.
N > Hey, would you like to get a house?
I think that if they wanted to do what you're suggesting with regard to the Baldurian tag, then Larian would need to establish through in-game dialogue early on that our character is from Baldur's Gate and that is an unchangeable fact. they also need to give us a chance to talk about the city more in act one so we as players can build up an affinity for it, otherwise any emotion they tried to bring about would come off as hollow.
Also with your suggestion I quoted above, a far better approach would be for us to address that in dialogue. Let our character talk to someone and tell them whether or not we had a house.