Artists absolutely do have a say on the matter, they can say no. They can not tour. They can only do small venues that don't use Live Nation. They can use other ticketing services - although the most expensive concert I went to this year was Rolling Stones and they didn't use Ticketmaster.

Artists choose to go with Live Nation because it makes them money, provides a better ticketing experience for their fans, and gives the artist a boogeyman to blame for high ticket costs. Pearl Jam tried to fight this fight in the 90s and realized that there isn't a better alternative if they wanted to tour and make money. They chose to keep touring and went back to using Ticketmaster.