There are simply too many dates on the baseball calendar and too many teams in the postseason. This pushes the start of the season into March and the end of the World Series to late October.
I also think almost every major sport has the same problem, for what it's worth.
I would almost consider splitting the League into two tiers, with Promotion/Relegation, like Soccer.
The worst teams get demoted to the second-tier, and the best teams in the second-tier get promoted to the Top League.