I'm just guessing based on how I perceive both games in retrospective. Dragon Age 2 feels to me not like to short a game but more like a to long an origin story. Story wise DA2 is necessary to generate a certain world state, which the overall story needs to continue. That is maybe one thing DAO failed to achieve, because afterwards the world was to stable to directly continue with the overall story arc.
So what DA2 basically does is setting of the world, introducing a charismatic main character, introducing an ancient evil, letting the Quanaries lose, filling the world with riddles like what is Flemeth and actually starting the Inquisition.
DAI in turn feels rather short in terms of main story. It is not as short as some people like to complain, I basically can't take people serious doing a speed run and after that start complaining, that they can do it in under 3 hours... but it still it is definitely not as long as DAO.
From this and the few things we know about the cancelled expansion, it seems very likely to me, that DAI is actually more like a DA2.5 and Hawke was supposed to be the protagonist. When you develop a story it normally starts with a few defining moments you keep, while the rest is constantly changing. We know from David Gaider that the Temple of Mythal was there in the expansion. Other moments could be blowing up the chantry and the conclave.
So my best guest is, that the way it was supposed to happen was Varric arranging a meeting between Cassandra and Hawke at the conclave. Maybe Cassandras reasoning was, that Hawke might be able to talk sense into everybody, but in the middle of it, things start once again to go south for Hawke. The anchor and everything might have been added after Hawke was skipped, to make the Inquisitor more unique.
The main goal for the story would have been bringing Hawke to the temple of mythal to basically set of the next story arc with some old gods on the run. From what David Gaider hat said, we can conclude that this version of DAI would have been much more tragic, than the lightweight version we got. Which in turn would be more in line with Hawke, as he is a rather tragic hero. Maybe Hawke was supposed to die in that confrontation along with a lot of companions, or he would have become the vessel for the dreadwolf making him the next antagonist.
So what would be different? I think the story would flow more smoothly and would have more meaning to it. Some quests would make a lot more sense and be a lot more tragic, because Hawke would constantly be reminded of what he set into motion. The overall story arc might be a lot darker and more in terms with the feeling of DAO. Obviously we would see a lot of different side quest, maybe wicked eyes and wicked hearts would not have happened or in a very different way, but the main steps of the story would be there.