First, a disclaimer:  I've watched football in general and been a fan of the Giants for fifty years.  I never played the game, so I know there are nuances that escape me.

My question:  Why do we have a fullback if he never ever gets a carry?

 It seems to me, that if you aren't going to allow your fullback to ever carry the ball, using him "only" as a blocker, then you might as well just go with two tight ends.  You could never fake a hand off to him that would be believed by the defense.  Being able to make a realistic fake to the fullback seems important to me, especially if you are a running team.

This is anecdotal, but my impression through the years, for the most part, is that the best running teams also had a fullback who at least occasionally carried the ball, maybe 4 or 5 times.

So, you football guys out there, help me out. Is this a dumb question?