I am not opposed to adding Hayate necessarily, but I think Team Ninja would need to be cautious. Ninja Gaiden should not just be an action DOA game----it is Ryu's game and story. Ryu needs to be the central focus and the more characters you add the greater the potential for watering that focus down. I think this gets particularly tricky with adding Hayate---another male ninja character who would be harder to make distinctly different from Ryu (as compared to the girls which are obviously distinct).
So, it would need to be done carefully. I think other characters should continue to only be playable in chapter challenge and trials.
My personal preference would be for a game with a greater emphasis on Momiji, Jo Hayabusa, Muramasa, Irene as the main secondary characters since they are more part of the NG narrative and story.