For the sake of this argument - let's say the Packers are the greatest team in the NFL for 6 years. They are so great that they cruise to a first round bye every season. And they have a huge edge against all playoff teams - so much so that they will win 65% of the time in ALL match-ups, no matter how difficult the opponent is.
What is the most likely # of Super Bowl wins the Packers will obtain under these circumstances over those 6 years?
Well, each year they have to win 3 games as a 65% favorite in each game. So the odds of winning the Super Bowl each year are (.65)^3 = ~ .2746
Meaning the odds of not winning the Super Bowl each year are 1 - .2746 = .7254.
Over 6 years, there are 64 possible combos of winning/not winning the Super Bowl:
Winning 6 = (.2746)^6 x 1 combo
Winning 5 = (.2746)^5 x (.7254)^1 x 6 combos (could lose year 1 or year 2 or year 3, etc.)
Winning 4 = (.2746)^4 x (.7254)^2 x 15 combos
Winning 3 = (.2746)^3 x (.7254)^3 x 20 combos
Winning 2 = (.2746)^2 x (.7254)^4 x 15 combos
Winning 1 = (.2746)^1 x (.7254)^5 x 6 combos
Winning 0 = (.7254)^6 x 1 combo
Using actual # instead of approximations....
Winning 6 = .0429 % or 2330.1 to 1
Winning 5 = .6799 % or 146.1 to 1
Winning 4 = 4.489 % or 21.3 to 1
Winning 3 = 15.81 % or 5.3 to 1
Winning 2 = 31.32 % or 2.2 to 1
Winning 1 = 33.09 % or 2 to 1
Winning 0 = 14.57 % or 5.9 to 1
Winning exactly 1 Super Bowl is the most likely outcome in this scenario.
And these are ridiculous circumstances. Injuries can easily ruin a season or at least cost a first round bye which make the odds of winning much much lower. Roster turnover over the course of 6 years makes it extremely difficult to maintain this kind of dominance. Not to mention that there are a lot of very talented teams in the NFL, one team having a 65% advantage over any team is very unrealistic. Edges are much smaller than that in reality. So all of the aforementioned numbers are going to be far lower. This is why even the most successful teams and players win very few, if any Super Bowls.
Take it from someone who roots for some pretty terrible teams in other sports - the Packers are awesome. They have won some incredibly exciting games over the years. They've made the playoffs 8 years in a row and won 1 Super Bowl - this is right at, if not above expectation of where they should be if you do the math. Don't let absurd expectations of winning several Super Bowls get to you. Enjoy what you have - it's pretty damn good.