I've said this in other threads but this seems an appropriate spot for it as well. In my opinion (and that's all we're doing is sharing opinions since we'll never know what BB and the coaching staff were actually thinking), here's what they were doing. They were trying to accomplish two things at once: (1) win the game, and (2) minimize the risk of injury to key players.
If they went all out for (2), which would have meant sitting Gronk and Brady in particular, they'd have completely forfeited a chance for (1), and I think BB wanted to win. But if they went all out for (1), they'd have employed a very different game strategy, and that would have exposed their key guys to greater risk (like hitting Gronk on seam passes).
So they went super conservative, aided by the Dolphins playing a lot of nickel (which made the choice easier), and they hoped that this conservative approach would be enough to win the game while at the same time minimizing the risk of injury to key guys.
After one half, they scored 3 points and were losing, and it was clear that this strategy could accomplish (2) but not (1), so they needed to change things up and try to win the game doing something different. Their first possession in the second half they went down and scored a TD, but after that they were ineffective.
It was a fine line to walk between (1) and (2), and there's zero - as in NO - chance that if they played that game again, even with the exact same rosters, for the AFCCG, that they use the same offensive strategy. I don't care what defense you're facing, you don't have Brady throw just 5 times in a half. In fact, in his entire career, that was the fewest pass attempts he'd ever tried in a half, so it was an unprecedented game plan for the Patriots. One that we will probably never see again. Certainly not in the playoffs.