Right, i've had some time to think about how to say this, and i think i have come up with a way to better explain what i mean. It's mostly going to be an example followed by how i view what happened in the games. I am by no means a professional writer (so feel free to disagree, i;d love to see your point), but i am an avid reader. From all the books i have read, i know what makes a plot strong and what causes it to be weak. The idea of this thread was that the current theme of the story does not fit with the desire for new characters every time. While i'm hesitant to say whether it will or won't work, i have to say i lean more on the side of the OP's main point. This will be from a "writing" point of view, because games are just a story.
First of all, a strong story is directly dependent on character motivation. They need a good, strong reason to be involved with the plot. For example, let us say we have 3 close friends who want to explore a haunted graveyard. Could they do it just because they want to? Sure, but it's not really a strong story. Instead, let us say they want to explore it because our protagionist's little sister went missing in it 3 days ago. Is that a reason to go in? It certainly is. Is it a strong reason? Yes, and it also provides us with a destination and a goal that our character's have right from the onset. In terms of Dragon Age, Origins and Inquisition did this very well. Regardless of how you felt on the matter, you were involved and it was a goal you simply could not ignore. DA2 was not really like this, Hawke's goal was to look after their family...that only indirectly affected their plot.
Let us say, that in the haunted graveyard, there are 3 paths. The path to the right leads you to a journal that indicates that children being lost to the graveyard is a very common affair, but there is something in the journal that implies it is not the child that is the target, but rather a way to entice the target to come. Suddenly we have an indication of a bigger affair, and that we are now somewhat aware that we are being intentionally lead down this path. The path to the left leads them to an abandoned cabin. Conversations deepening the characters relationship may occur, and let us pretend that by the end of this, we feel deeply for the friendship between the three, and we agree with their unanimous desire to save the little sister. There are subplots that link into the final affair, keep the reader interested, while foreshadowing what will happen. Happened in DA:O and DA2 led us into the event of DAI, one concluding the other.
Eventually on our journey through the haunted graveyard, we reach a pivotal point in the story. We find out that one of our friends is under the control of what stole the little sister. A fight occurs, but they escape before we have a chance to strike them down or gather answers. We now have a chance for our characters to reflect, but a new emotional drive to stop the events. Suddenly, the character's motivation has changed from wanting to help their sister, to wanting to stop their friend. Obviously, their original goal has not changes, but now we have a deeper connection to the events. But let us say, after the sister is saved, we simply leave the graveyard. We don;t stop the friend, we don't stop the evil. A few years down the line, someone else just happens to stumble onto the evil and they stop it out of a sense of duty. Is that a good reason? Sure. Was it as satisfying as having our hero previous stop the events surrounding their story? Probably not. Could they give us the same emotional drive as we had before? Not likely, they have no connection other than "Well, i might as well".
Getting towards the end of the story, what should happen is that the character should resolve all loose ends. Save the sister, stop the friend and get rid of what ever evil draws people there. This is what makes a story strong. (my story is rubbish, i know, but it's just an example). Looking at the Solas story from the perspective i have just shown, it makes that story weak. We lose the character motivation to stop him. Not completely. But i ask, which motive is stronger 1) We need to stop the bad guy that just showed up or 2) we need to finish what we started and save/kill our friend who is about to make a horrible mistake. While both have a motivation, one has a much stronger, much deeper connection to the events and as such is far more likely to have motivation to stop the "big bad", and with a much more satisfying result.
Sorry for having to make it a little off topic, but i just thought it would make my point clearer is i separated from "this story" to "a story", and i hope this helps people understand the point more. What is being said is much more out of concern for the story rather than being for or against new characters.