As the rules have favored passing, defenses have evolved to stop the pass.
Thus LB's are getting smaller and faster, as others have noted.
So the Patriots have built an offense that can spread the field to take advantage of these rules, and also that can pound your smaller faster defense with a power attack. A couple reasons:
One, the Patriots love to create mismatches. That's why they gameplan so much. There are two basic philosophies in coaching football. There is the: we are going to train a couple of plays so many times that our players can run them perfectly, and tell you to line up and we will run this perfectly time after time. Dungy espoused this at Tampa Bay (there's actually a good description of this in the book "Habit.") Then there is the game-planning approach that creates uncertainty - you don't know what is coming. This is one more way to create mismatches - when you face a smaller "Tampa Two" defense, play an OT at TE and bring in the FB. If they go goal-line, the FB can run into the flat.
Two, the Patriots have not been strong protecting a lead since the Clock Killer. It's harder to be successful in the six-minute offense without a power running game. Bringing back a professional fullback improves your fourth quarter clock killin'. As others have noted, putting a big lineman in that role is risky for multiple plays. A defensive lineman is basically training to avoid contact, to slip past the OL. The offensive lineman is basically training to immediately engage and mirror or move the opponent. The FB is a ram, training to get up a head of steam and blow up a defender.
