They don’t “own” the venues so much as they obtain exclusive rights to all events being held at a facility which is worse. Dump trucks of money to venue reps are probably at play here.
They also are part of the same company as a big promoter so a venue which doesn’t go along with them has to worry about losing the most popular acts, too. They prefer pre-packaged slates so that can be a big difference: play the game with Ticketmaster and you’re basically booked full
with popular acts, or go it alone and have to spend more time finding bands on your own.