In response to zbellino's comment:
Knowing BB, it's a host of small reasons that justify it.
1.) He helps them scout teams with running Qbs.
2.) He makes teams have to prepare *something* in case he plays, because the O is so different with him in it, even if it's overall very inferior. Any resources a team wastes are wasted. All the Pats need to do is flash one or two option plays, and opposing teams have to prepare like they have many more.
3.) He contributes on special teams/depth at FB etc. Using him on punt protection, though, is something I'll add they can continue to work on. Because he is expendable, you don't worry about him getting injured, but he can throw a lot better than a RB, and run a lot better than a QB, and has a frame that could block. Trick plays could be an option.
I'd cut him too and get a real third stringer, but hey that's me.
The 2nd point I see where people are coming from but in reality no team is going to plan for a couple tricks plays when they are facing Brady. If I was the opposing DC I'd actually hope BB took Brady off the field and brought Tebow in, not be worried how to plan for it. I'd just tell my guys if both are on the field 1 guy has to watch Tebow for the draw otherwise treat it the same as if Ridley or Vereen were back there and Brady might throw the ball and dare BB to use a plan which Tebow threw it. I honestly don't think any DC would give more than 30mins to planning for Tebow at any point during the week as I doubt BB gave more than that when Tebow was on the Jets.