For most events (at least in the US), you can only get tickets via TicketMaster. Venues sign an agreement with TM that forbids them selling tickets elsewhere. TM controls venue's entire ticket sale workflow, including inventory, printing and sending tickets, etc.
Going with another vendor is a gigantic undertaking, you would need to overhaul most of your processes. Most venues don't have the resources/bandwidth to pull that off.
Ticketmaster pay a substantial share of their "service fee" to venues and promoters. By signing an exclusivity deal with TM, venues can guarantee themselves a greater share of the effective ticket price. Artists are powerless to negotiate because of TM's dominant position in the ticketing market. It's a grubby little money-go-round scheme that exploits artists and fans alike.
Sure and it's the same on the artist side. If you want to tour you can not avoid Ticketmaster. Remember Perl Jam at the height of their popularity and powers tried to take them on and lost:
Going with another vendor is a gigantic undertaking, you would need to overhaul most of your processes. Most venues don't have the resources/bandwidth to pull that off.
And that's how TM stays a monopoly.
Source: used to work for a large venue.