You can't compare those 2 situations. First, the running plays would have to be able to produce the same average yards par play than a passing play which is not the case. Simple math : even if you average 5 yards per carry, which is great, almost all NFL team, if not all of them, are averaging more than that on pass plays. Therefore, the chances of limiting an offense to less than 10 yards on 3 consecutive plays is greater if the offense run 3 straight run plays rather than 3 passing plays.
Also, as I mentioned, great running teams have historically not done so well. If memory serves me well, from the CHFF article, about 50% of the 25 greatest running teams of all-time didn't even make the playoffs. So even if you say that the shotgun type offense is not so great to win championship, it is at least better to get you to the championship game than a great running game.
Finally, there's wear and tear with every NFL players over the years. But are you serious when comparing a running back who gets hit at least once per carry (or very close to that rate), therefore about 300 times per year, to Tom Brady which at the most got hit 86 times over 2 years (according to the dubious stats from ESPN) ?? That is just crazy...
By the way, the only other time that Brady might have missed a game (other than last year) was in 2002 under Weis and the 'standard offense'. Even if they had qualified for the playoffs, Brady would not have started in the playoffs because of a bad arm. So making the assumption that only the shotgun offense is the reason Brady's injuries is not accurate.
Now the last thing...as great as Brady is, if the offense has to be radically different for him to be able to play, then it's time to move on to another QB. It's harsh, but that's the way it's always been in sports. As I said, a great running back will only produce 5 yards per running play, while any second string QB will produce more than 5 yards per passing play. So if you have to run more than you used to in order to protect your QB, this is not going to help the offense and therefore the team. It's a sign you have to change your QB, even if it's Tom Brady.