It is a good fit.
But is it really? Do they play anything close to the style of offense that he needs to have a chance at being successful? That, IMO, is the biggest impediment to him getting signed, even apart from the baggage. S.F.'s system under Harbaugh was designed to play to his strengths, and while he was able to hold it together, he thrived in that system. But outside of a system like that, he seems to really struggle.
I'm not disagreeing with you, but I'm not sure how critical that is. When someone first brought it up I immediately thought of Jacoby Brisset. He's a lot closer to Kaep than he is Brady. Garoppolo seems to be a midpoint between them. NE is not going to run the same sort of offense if Brisset has to play. And there are other examples of this, as well. The Patriots started a game last year with Edleman as their backup QB. They've started games without the requisite number of O-linemen. Your gameplan reflects the tools at your disposal. I realize that Harbaugh is no Belichick, but he might well top the list of non-Belichick/Carroll coaches. He's perfectly capable of fielding a team that can improvise and change styles as the situation dictates.
edit: Expansion of King's ninja post.
No argument with any of that, but I'm still of the opinion that until it happens (and we may be close, I'll give you that) that style of QB is awesome the first time through the league, and not so awesome second through infinity. Cam Newton was stopped when he needed to be, Kaepernick was stopped when he needed to be, Wilson (who can play "Brady" better than either Newton or Kaepernick combined) was stopped when he needed to be... Brady was not. You look at that list of QBs, and while you can quibble with individual rankings, there are a TON of QBs in the mold of Johnny U, there are, essentially, none in the mold of Randall Cunningham.
I think there is some incentive; I can see Jim calling John and raving about the kid, but I think, generally, if they do that, it's not a good move. I think we're seeing the real Kaepernick over the past couple seasons, and not in that one glorious, "oh-so-close" season.