I don't really get how they're "not introduced properly." Their roles in the story are mentioned prior to the quest where you meet them. Celene is the Empress of Orlais and Gaspard is the noble vying for the throne. Briala isn't mentioned by name, but Josephine does reference a third group of elves that are drawing out the civil war. What more is needed?
Did not playing through the Dwarf Noble origin leave you incapable of deciding between Bhelen and Harrowmont?
You just answered yourself. You can talk to all of Orzammar about Bhelen and Harrowmont. You have time, you work for them and you see how they work. That's an introduction, it tells you a lot about their characters even if you aren't a dwarf yourself.
Nothing like that happens with Celene, Briala or Gaspard. Even the civil war is only mentioned, despite the Inquisitor running around on the Exalted Plains. I think I helped some soldiers with the demons but don't ask me what side they were on.
What more is needed? Well, how about -anything- that would allow me to form an opinion about them? You meet each for a few minutes. Should I make Gaspard king because he says he hates the Game? Should I allow Briala access to the throne because Leliana tells me she used to be Celene's lover? Should I support Celene because she's the rightful queen? That's basically all I know about them. Oh, I am sure there are probably some more info tidbits somewhere in the palace but you don't exactly have time to explore it, do you?