The entire ethos of Bill Belichick's coaching is to Not waste your time going against a planned Defense. It is why he gameplans and changes the Team's personality every week. BB's approach is anti-thetical to Lombardi, who said, "Here we come, you stop us, if you can. Lombardi wanted to out execute the opponent.
If he were Carrol, BB would not have run into a stacked goal line Defense either, especially as the Pats have some very big DTs and LBs.
BB tries to run when he has the advantage there; and pass when he has the advantage there.
I fully believe that Belichick would have done the same.
I agree, however I think brady and McDaniels would have done a much better job executing/made it a low risk play, such as edelmans goal line route or a fade to gronk.. where it would take a miracle to pick us off.
This whole time issue and need to throw was self inflicted. They had the ball on our 1 line with a time out and minute to go..which is like an eternity from there. They were so concerned with not giving the greatest qb of all time another opportunity that they forgot they have to score first! Carrols only priority should have been getting in the end zone.