I have some recent experience in live events and I can tell from the comments here that most people don't understand how the economics work. Don't feel bad, I didn't either until I was involved. It's... confusing.
We all think that when Major Band goes on tour, they just rent a bunch of big arenas and sell tickets. If you think that, a lot of the comments about the bands getting paid by TicketMaster make sense, but that's not at all how it works.
Venue operators are a lot like commercial landlords. They manage a building, and someone else runs all of the businesses in it. Major Sports Team might play in an arena they own, or an arena owned by the city they are in, or one owned by a third party. Major Amphtitheater could be owned by an investor group, LiveNation, or (as in my area) a symphony or other not-for-profit or governmental entity. Whoever owns it, they usually contract out basically everything that goes on inside it, just as an owner of an office building or strip mall doesn't own most (or any) of the businesses that have offices or stores in it. That beer you bought probably was sold to you by Legends or Aramark or Delaware North who payed Arena Owner for the food and beverage (f&b) rights. The F&B might then be subcontracted out, done in house, or some combo. The F&B company might sign an exclusive deal with Bacardi to use their liquor brands. The shirt you bought probably was sold to you by the exclusive merchandise vendor (or, with music, likely the space was given to Major Band as part of their contract). Etc.
The events work much the same way. The venue doesn't run the conerts, they don't even book them, hell their owners likely couldn't even tell you who was performing yesterday. They probably have an exclusive deal with a large promoter like LiveNation, AEG, etc. Or they may not be exclusive, and various promoters may rent venues on an individual basis. For each concert, a promoter pays the venue and hires Major Band. My favorite band does about 75 shows a year, and gets paid $1 million per. If nobody shows up, they still get $1 million, though they probably won't get it again next year. They don't really know or care what the ticket sales are, except maybe to use it to ask for more than $1 million next year. Then the promoter sells the tickets and they profit from the difference.
But, the venue or an exclusive promoter may have a deal with a ticket seller like Ticketmaster. And because Ticketmaster is owned by LiveNation, the biggest promoter (by far, about 2.5x the size of their nearest competitor) and also an owner or exclusive operator of most of the nation's biggest venues, the ticket seller may BE the promoter AND even the venue. Even worse, LiveNation does band management too. They've been caught steering their bands away from arenas and amphitheaters with a third party promoter after the venues signed ticket deals with other ticketing agencies.
LiveNation's business model is very simple (and brilliant and evil): they buy out venues. 50% of the world's concert revenues come from like 300 venues, so it's an obvious chokepoint. They pay Venue Operator millions per year to run the facilities, then they hire Major Bands to come play there. They make money off the concert and the TicketMaster fees. Or, in cases where for whatever reason they can't buy out promotion, or own the venue entirely, they pay whoever does to be the exclusive ticket agent, so they still get that sweet ticket money.
So why does Ticketmaster like scalpers? Simple, more fees. In the good old days, Ticketmaster sold a piece of paper once, then whatever happened happened. Then came StubHub who made a trusted digital route for reselling tickets (that themselves became digital). At first Ticketmaster fought them but then eventually realized it was a whole lot more profitable to just do it too.
If you buy a ticket and go see the show, they only made one ticket fee off of you. If you buy a ticket and then turn around and sell it verified resale, they got paid twice.
The obvious question is: why don't promoters just charge more for tickets to shows that sell out? (Caveat: the following is more supposition by me than the above.)
1.) Bands don't like this. Bands want their fans to remain fans, so they will buy albums, stream music, buy merch, see future shows, etc. for years to come. If the Stones have shown us anything it's that a music career can span generations if you manage it right.
2.) Just as night clubs purposefully keep a long line in front of the door even though they're empty, a quick sellout induces demand, so it might seem like Taylor Swift's promoters could probably 6x her price and still sell out, but that's likely not true. Bands even often have price restrictions in their deals with promoters.
3.) Most of the time the promoter and the ticketing agent are the same company, so you might as well shove all of the blame onto TicketMaster. LiveNation knows you hate TicketMaster but you'll keep buying tickets from them as long as you have no other choice, so they just keep the rest of their brand behind the scenes. You probably don't even know who promoted the concert you went to, and they like it that way, but you know who charged you $30 in fees.
4.) They get other per-head revenues from their contracts with companies like whoever does F&B, sponsorships, etc. This is why low-selling shows often give away tickets for free, or why you'll see tickets on Groupon when a band plays an amphitheater that's a little too big for them. An almost sold out crowd at $110 a ticket might make less money than a sold out crowd at $100 a ticket.
In any case the one thing you can be sure of is that they have analyzed the data and priced everything at whatever makes them the most money. They're evil but they're far from stupid.
But as to why Major Band uses TicketMaster: TicketMaster has exclusive deals with over 2/3 of the big venues in the US, is usually the promoter that hired them and may even own the whole damn venue.