I think it would be kind of interesting... if The Warden remains somewhat of a mystery. I'll paint a scene.
Inquisitor and allies are battling a "thing" - some insanely powerful "thing" and they're losing (maybe once your party loses half it's members?)
Then a cut screen - Inquisitor is on the grounding shaking off the last attack when a figure hurtles past him/her and into the fray. (Cut to designing your Grey Warden)
For a moment - the Inquisitor watches as a Grey Warden holds off the enemy. Then - you rejoin the fight.
You fight with your Warden through a crazy battle.
After the conflict, you can speak with a few friends... while off in the distance, Leliana, Morrigan and the Warden speak outside of listening range.
Then your Warden comes up to you.
"Morrigan/Leliana (depending on if you romanced either) said you could use some aid. I'm afraid I can't stay... there's trouble to the north. I'll do what I can to help until you've fixed this mess. Good luck."
Then maybe - you can meet up with Morrigan and/or Leliana afterward.
"So, THAT was the Hero of Ferelden eh?
etc. etc
Then - your Warden hops onto a horse and takes off.
The voice actor would never have been yours to choose anyway - and I would actually find it humorous if people who claim voice acting is superior would be upset at having their imagination usurped on this topic.