In the past 5 seasons, the only SB participant that passed more than 55%, during the regular season were the Broncos 59% pass. The falcons were exactly 55% pass. The others were all under that, and Carolina actually ran more than they passed by a small margin.
Where are you seeing all these pass happy SB teams?
First of all, I am not saying teams aren't or can't be balanced running and passing to be effective. Of course it can be very effective in keeping the defense honest, wearing out the defense, setting up the play-action, etc... However, teams can and do succeed being pass happy. Particularly in 2004 when refs starting enforcing the don't touch the WRs beyond 5 yards past the line of scrimmage and rules, play design and QBs coming into the league are so much more advanced than they used to be.
The numbers you are using are skewed and ignoring situational football. The main reason teams that win games look like they are more balanced in pass/rush is because teams with the lead in the 4th quarter tend to run the ball to run out the clock and teams that are losing in the 4th quarter (and much earlier if they fall behind significantly) is to try move the ball down the field in chunks and score more quickly. So to take the final numbers of the season and simply come up with a pass/run ratio and conclude that teams making the playoffs because they have a better pass/run ratio is misleading. Teams that make the playoffs may have a better pass/run ratio because they are more often than not leading in the 4th quarter and relying heavily on the run to wind down the clock whereas teams that don't make the playoffs are more often trailing in the 4th quarter and rely heavily on the pass to make big plays and conserve time on the clock.
For example, looking at the defending SB champion Patriots last year in their 5 losses they passed the ball 193 times (attempts + sacked) and rushed the ball 111 times for a 63.5%-36.5% pass/rush ratio. However that ratio includes the Patriots passing the ball 44 times and rushing the ball 16 times (the last 5 plays against the Titans the Pats rushed the ball all 5 times conceding the game to the Titans trailing 34-10) when trailing in the 4th quarter. That is a pass/run ratio of 73.3%-26.7% and if subtracting the 5 rushes against the Titans that ratio would be 80%-20%.
The 11 regular season games the Patriots won they passed the ball 394 times and rushed the ball 367 times for a 51.8%-48.2% pass/rush ratio. However in the 11 games they won in the 4th quarter the Patriots passed the ball 72 times and rushed the ball 123 times for a 36.9%-63.1% pass/rush ratio. Not a single game of the 11 wins did the Patriots throw the ball more than they rushed it.
Keep in mind teams with sizable leads at halftime will often rely heavier on the run to begin the 2nd half.
Some in game examples of how numbers are skewed...in the "Miami Miracle" game the Patriots passed the ball 6 times and rushed the ball 2 times when trailing in 4th quarter for a 75%-25% pass/rush ratio and when the Patriots had the lead in the 4th quarter they passed the ball 4 times and rushed the ball 7 times for a 36.4%-63.6% pass/rush ratio.
In the Steelers game in which the Steelers won 17-10 and led the entire 4th quarter against the Patriots the pass/rush stats heading into the 4th quarter for both teams....Patriots passed 20 times and rushed 16 times for a 55.5%-44.6% pass/rush ratio whereas the Steelers passes 30 times and rushed 14 times for a 68.1%-31.9% pass/rush ratio. In the 4th quarter as the Patriots attempted a comeback their pass/rush was 17/3 and the Steelers trying to run out the clock had a pass/rush of 6/11. The outcome of the game was Patriots had 37 pass and 19 rush for a 66.1%-33.9% pass/rush ratio and Steelers ended the game 36 passes and 25 rushes for a 59%-41% pass/rush ratio. Clearly in this game the Patriots had the more balanced play heading into the 4th quarter. However, because the Patriots were trailing the numbers at the end of the game look like the Steelers clearly had the more balanced play throughout the game which is absolutely not true.
Your example of the past 5 years conveniently included the Patriots who were 40% of the Super Bowl participants and Brady's game management and Patriots are exceptional at both pass and run. As far as being able to run the ball effectively the Super Bowl teams are all over the place over the past 20 or so years.
Since 2001
Where Super Bowl winners ranked in Yards Per Game (YPG) since 2001 respectively (13, 27, 27, 7, 5, 18, 4, 23, 6, 24, 32, 11, 4, 18, 17, 7, 3, 5)
Where Super Bowl winners ranked in Yards Per Rush (YPR) since 2001 respectively (23, 26, 30, 17, 12, 16, 3, 29, 5, 25, 32, 12, 12, 22, 13, 25, 4, 20)
Where Super Bowl losers ranked in Yards Per Game since 2001 respectively (5, 18, 7, 24, 3, 15, 13, 32, 32, 11, 20, 4, 15, 1, 2, 5, 10, 3)
Where Super Bowl loser ranked in Yards Per Rush since 2001 respectively (1, 11, 16, 8, 2, 23, 11, 31, 30, 17, 21, 3, 20, 1, 10, 5, 12, 3)
* Prior to 2001 between 1970 (merger of leagues) and 2000 (31 years) only 4 times did the Super Bowl winner finish out of the top 10 in YPG (70 Colts = 23rd; 78 Steelers = 14th; 81 Niners = 19th; 96 Packers = 11th). The game has changed.