Ultimately WE are the protagonist. Whether we are driving around the meat covered skeletons of the HOF, Hawk or Inky, they are only tools we use to continue in a story. A character in one segment of this story betrayed one of my meat covered skeleton vehicles, so either patch up my current dinged up beater, or get me a new vehicle, matters not, because I, the protagonist, will deal with the betrayer no matter what vessel I have to use to do it. It makes sense that Inky would continue to be the vehicle I use to go off and stop Solas, provided this is what the next installment will be about, the fact that it has been stated by the devs that Inky won't be, then it is plausible (not definite) to conclude there may be more to the story than just Solas.
To the extent we are role playing, emotionally engaging into the current representative of ourselves in digital form is dependent on our individual ability or desire to see this as a game with a story or a story played out in a game. A good writer can make a person feel like they are in the story or even a part of it, but with a game, we actually are, whether the story is written well enough to make us feel this or not.
The OP states that "New protagonists every game dont work with current game foundation", I simply disagree on two levels. Firstly, I am ultimately the protagonist in every game I play. Secondly, it clearly works with the current foundation because every game thus far has had a new character representative of me the protagonist, and every game has been successful, we only need to look around any given forum to see this. The developers think so, I think so, and millions of fans apparently also think so.