Yeah, but in Bioware's head cannon, the est path, the Hero of Fereldan sacrificed herself to kill the archdemon, so I'm sure HoF Quizzy was off the table. It would be nice to see my HoF, Hawke, or Quizzy get together in DLC or DA4.
Personally, in my head cannon, my hero stopped the blight, dark ritual, warden commander, killed the Architect, killed Flemeth, was besties with Morrigan, romanced Zev, won land for the Dalish (I liked to think my Hero convinced her clan to travel back to Fereldan after the events at Kirkwall, including Merill, and they were living in the Dalish land in the Hinterlands.) I got many ties to the continent/country. See, having the HoF being Quizzy would be no problem for me, but I know for most people it would be.
I love the Darkspawn Chronicle/ Hero of Fereldan Chronicle idea. It might sell more than the original DAI.
That's Gaider's canon, yes--and only a Dalish Warden in his canon.
However, at the end of DA2, even with a dead Dalish import (default canon) or a dead Warden (HoF) import (which in my case was co-incidentally my Dalish female), Leliana still says they looked for "The Warden" first at the end. In this case, it's intended to be the Warden who is sent from Orlais to Amaranthine as the new Ferelden W-C [for Awakening]. (theories state it could also refer to Alistair or Loghain if they lived but since you referred to canon, in Gaider's canon, Alistair is King and Loghain is dead, so no).
However, the Orlesian Ferelden W-C does everything in Amaranthine that your Warden would do: kills or handles the Architect/Broodmothers, saves Amaranthine (and/or the Keep), builds the Order in Ferelden (even with the hamstring of being an Orlesian), and manages to end the darkspawn threat in Northern Ferelden while keeping a good relationship with the new King, being the Arl/essa of Amaranthine and possibly keeping Nathaniel Howe alive (which, in turn, keeps Fergus Cousland alive). And that's on top of whatever they've already done in Orlais (it's unclear/not stated, but obviously the Orlesian Ferelden W-C thinks they are diplomatic enough to try it, even with the strained relations between Ferelden and Orlais).
Still more experience than Hawke. 
ETA: With Alistair as King, in his King Alistair cameo (as in Gaider canon, Ali is, of course, KoF), he says to Hawke that the only thing he wants Hawke to do is to "look after Kirkwall" because things are a bit rough between Ferelden and Orlais (which implies that he doesn't want any further ruckus there, either) and there are still lots of Fereldens in Kirkwall. Of course, if you play MoA DLC, Hawke goes to Orlais and kills Prosper (usually), making relations that much more difficult, and then comes back and has the Chantry blow up because Hawke couldn't rein in either Meredith or Anders. I always think of King Alistair back in Denerim doublefacepalming and saying, "dammit, Hawke, I asked you to do one thing..."