I dunno. I think there's something to be said for a fresh start each time. It's fun to continue where you left off, but I think you start to accumulate a lot of narrative baggage as you progress from one game to the next. I definitely wouldn't want to drag the same character through more than a trilogy, and it would still need a solid overarching story. The original trilogy did that very well I thought: discovering the Reaper threat --> pursuing the Reaper threat --> ending the Reaper threat.
The Dragon Age forum gets a lot of talk about closure, but you can't really get final closure on your character unless they die. At some point, you have to just have to let your head canon take over and imagine whatever future you want after the character walks off into the sunset.
All i can say about DA style new protagonist every game is its ****.
Thrust into a new story same setting with recurring themes and characters. Only you're forced to start all over getting to know the protagonist again. Which in turn takes up half of each game as they try to make them relatable.
Make a character, make them relatable, then take them on a journey.
If every story has a beginning middle and end, soneone forgot to tell Dragon Age, they just do multiple beginnings.