No but appart from festivals (which were not relying on ticket master) I haven't seen tickets sold by only one company. Usually there are different ones and also some plain old in person in ticket office of department stores.
There are venues that are Ticketmaster specific because Ticketmaster's parent company owns the venue and some acts just use Ticketmaster because they are the most popular ticketing service. If I want to go to UFC 292 for example, I have to get my tickets through Ticketmaster. UFC isn't using some service that shows up on indiehacker
