The reasons for Hawke over Warden are abundant:
1) Hawke is involved in the Mage-Templar war and was accomplice to the triggering even that set it off to begin with.
2) DA2 was supposed to have an expansion titled Exalted March. It nevertheless was used to fabricate DAI's plot and certain plotlines only make sense if Hawke is involved. The Warden is relatively independent of the plot.
3) Hawke is always alive. The Warden can potentially be dead via killing the archdemon.
4) Hawke has one origin and can only be of one race and two genders. Class is irrelevant. The Warden can be of three different races, each with up to 3 origins, and two genders.
5) Hawke has two VAs while the Warden has more than a dozen.
6) The Warden is an avatar of the player that was very, very malleable. Hawke was a character with defined personalities and can only be directed by the player.
7) Barring specializations which have been revamped anyway, Hawke is closer to the DAI character build than the Warden's in DAO. If they wanted the Warden to participate in the Inquisitor's party or even played by him, there would be a much more significant amount of "retconning" of abilities. Hawke is more manageable.
All in all including the Warden directly is not only immensely more work, but would actually be way more forced than Hawke could ever be. Be glad they aren't sacrificing story integrity to bow down to your whims.