This is not how concerts work, and artists and producers don't get any money from Ticketmaster fees. In most cases, a promoter pays an artist a flat fee to perform. The promoter then markets the show and gets the ticket sales, and Ticketmaster gets Ticketmaster fees.
Unfortunately Ticketmaster is owned by LiveNation, and they are far and away the biggest promoter. They sign exclusive rights with large venues. My local 25,000 seat amphitheater has a deal with LiveNation. I can only get tickets to shows there through Ticketmaster.
Artists hate Ticketmaster too (some have sued them) but if you want to do an arena tour, good luck avoiding them. Artists use them because they don't have a choice. The number of large venues that don't use TM is growing, my local basketball arena uses SeatGeek.
The one concession TM makes is to their fan clubs. Artists get to sell tickets directly to a limited number of fans. If you love an artist, joining their fan club will probably save you the annual fee back in one show.