I think the lack of 3 peats is more a result of how much of a crapshoot the playoffs are in baseball. A dominant 162 game season can be destroyed because a single reliever has a bad inning in a short series.
Baseball's problem is that the current system is set up to favor a few large market teams. There are a lot of small market teams that have to be terrible for a decade to set up a competition window of 2 years. Teams like the Dodgers and Yankees can just spend until they're good. It doesn't guarantee championships (nothing can in baseball) but it usually guarantees they're competitive.
Even if your team sports a $100 million payroll in baseball, you have teams outspending you by 2.5 times. That's a problem.
I think MLB sees expanding the playoffs as addressing it. It doesn't.