In summary, I think we can say:
Championship teams rarely have any glaring weaknesses, i.e. they're rarely BAD at anything. Every aspect of the game (run/pass defense, offense, run/pass special teams, playcalling, depth) only helps your team's chances of success, and excelling in any one given field only helps the rest of your team. Having a glaring weakness in any one given field only hurts the rest of your team.
No, you don't NEED an elite defense or running game to win the super bowl. But it sure as hell helps, and if you're only okay you'd sure as hell excel elsewhere.