I'm guessing leagues don't do it because of the economies of scale and the fact setting up a ticket selling framework isn't their core competency. Look at how all the major sports leagues have allowed Fanatics to take over their official merchandising, another non-core competency area for pro sports leagues/teams, in the last five years.
As much as I dislike Ticketmaster, there would also be some logistical challenges with setting up concerts at larger venues, some of which are concert-specific venues rather than arenas or stadiums, if a large promoter like Ticketmaster didn't exist. That's why many more popular bands partner with Ticketmaster/Live Nation when setting up their tours. Even in cases where independent promoters organize concerts, like I.M.P. in the DC area, those promoters usually oversee more than one concert venue, and the largest indie promoters operate multiple venues of different sizes and configurations (indoor/outdoor, mostly reserved seating/mostly general admission standing, etc.).
