There's a slight difference here. 1) He went from "full time" to 46 snaps over 15 games, and 2) the team kept promising him a bigger role, and he asked to be released back in training camp if he wasn't going to be used at all which is how he saw things going down (which is what happened).
The Pats played him full time because they were desperate. In a truly limited role, 15-25 snaps a game, he may still be effective. And he may be happy with that role. Belichick and Harrison just have to be honest with each other about what they want and envision, and from the scuttlebutt over the years, that is one of Belichick's strengths when compared with other coaches.
While I get what you are saying I really want them to use that spot to get younger, faster, more athletic. This team can’t stop mobile QB’s and Belichick has to fix that problem.