I agree that scoring is obviously the most important aspect, and that is much more likely to come from flexibility, but let's not push the 50+ attempts winning percentage farther than it may go.
There's little doubt that the ability to run the ball is key in most situations, particularly when it may be part of a larger gameplan that equates to chewing up clock, sustaining drives, and keeping the opposing QB off of the field. More importantly, when the defense is giving you the run but you still can't pull it off (2010 nickle formation from the Jets), or weather may call for the need to abandon some portion of the passing calls due to practicality (games involving lots of rain/wind).
I'm not calling for "balance" simply because I don't like winning via the pass, but more so due to a concern that we'll need to successfully run the ball in the postseason. I don't think this is unreasonable, although your chart of overall team rankings in the SB certainly helps to alleviate some of the worry. While we have a much improved defense which ranks highly, I don't think we have anything close to the teams in the past that helped to mask the running game deficiency entirely like maybe 2003.