You're pretty much correct, and that's more or less what I've figured out over the years. The 1991-92 Redskins were pretty damn close to being what I'm looking for... 14-2 regular season (should have been 16-0), dominant offense and defense (ranked 1 or 2 in both), had a dominant playoff run, including clubbing the Bills in the Super Bowl. That team set records for scoring, offense, defense, and just generally clobbered opponents all season long. Their two losses were in Week 11 (to Dallas) in a game they should have won, and Week 16 against Philly when Joe Gibbs took out almost all his starters in the second half, allowing the Eagles to kick a last second, game-winning field goal.
I have to respectfully disagree with your view of what sports is supposed to be. Of course that is likely due to my extreme competitiveness and control issues combined with my own personal sports/competition record. Without getting into details, my first even mildly successful competitive endeavours were in high school, despite the fact that both of my younger brothers were exceptional athletes. I learned early in life the difference between winning and losing and it has seriously molded my view on this issue.