I hope there will be no happy endings. Not canon, anyway. Everyone's entitled to their own headcanon, but the game itself showed us, I think, that there are no ideal solutions in the long run. It's dark fantasy, it's supposed to be dark. Avernus might be able to do something about the taint, but it's years away unless you let him perform experiments on living people (if you do, then well, it's hardly a happy ending if it's build on torturing people).
In my personal canon Warden&Alistair will face a revolution when they don't produce the heir to the throne for a long time, and will either need to implement really harsh policies that will put them down in history as bloody tyrants or abdicate. Or, well, get killed, plunging Ferelden into an age of succession wars.
Malewarden and Anora might have a happy ending, because Bryce will probably help if there are problems with the heir >_> Or Anora would find a way; she's a smart woman. She'd find a stable boy that resembles the Warden and take care of it
Regardless, I don't think the Warden will really feature that much. The game's not about them. For all the DAO geeks who played through all the add-ons and the dlc and made a 'perfect' save any reference to our decisions will be squee-worthy, but I imagine people who will come to the game for the first time will be sort of 'huh? why should we care?'