Yeah, this is going to be a cluster. Ticketmaster is definitely a problem, but all of these venues signed contracts with them, and then Swift chose what venues to book knowing that meant she'd be dealing with Ticketmaster. It's not just Ticketmaster that's the problem.
So many layers to this one too. The fees are ridiculous. Ticketmaster needs cut down to size on that front alone, but I don't know how that gets regulated. You can't set max fees easily.
The ticket prices, which would have been set by the artist's team, were insane. And that's important to remember. Ticketmaster didn't force them to charge $100+ for nosebleed seats. The best I can tell they also didn't announce prices in advance, which is a pretty shady move. The artist could have announced prices but didn't. You ended up with people going through the process to get the pre-release code, then waiting online for a long time that day to get tickets just to find out how overpriced it was. But that's another problem. You can't regulate what artists charge for tickets.
The, probably, biggest problem, was putting all of the tickets on sale at the same time. There was no way their system wasn't crashing. They knew it was going to crash. This has happened before with other tours with them. Why would they not stagger the on sale times? If they do that, this probably isn't happening right now.
There's no fixing the scalping. They can make it harder to transfer tickets, but they can't make it so you can't transfer them at all. At that point you are going to have people running the prices up.
As for the Ticketmaster "monopoly", I don't know what can be done there. I don't know this truly falls under monopoly as there are other ticketing companies and other venues that use them. Even if you make the argument that they are, what's the fix? You can't have more than one company selling tickets for the same event. It would be impossible to control inventory. Individual venues really need consistency too for ticket processing, so having different ticket companies sell tickets for the same venue even if it's different events isn't ideal. And, if you are putting a tour on, doing dozens of events across the country, it's much easier to deal with one ticket company than multiple. Even if you figure a way to split it up or open it up to multiple companies, you will still end up paying a $10 or whatever fee for a ticket. It'll just change what company gets that fee. The "competition will lead to smaller companies charging less" argument is nice in theory, and it would do that right off the bat. But over time, dealing with hundreds of thousands of tickets and all of the online and on site processing isn't easy. The first time one of these cheaper companies screws up a major tour's tickets because they couldn't afford the tech staff or bandwidth, they are done. So you end up with companies charging more to cover the infrastructure, and bigger companies surviving while smaller companies fade away. That's why Ticketmaster is where it's at. They can handle, almost, any event. Artists accept the huge fees that just get passed on to their fans because it's easier on them.
It'll be interesting to see what happens. I think the Justice department and/or Congress eventually looks the other way as this is a mess. There's not an easy fix. Lawsuits are another game completely. I don't know what change a court could force either, but you never know on that. I don't know enough of the legal argument of pain and suffering from not getting your tay tay tickets to say how much teeth that has. I suspect one of the changes that ends up happening is Ticketmaster ends up changing their fee structure so that the fees get moved from the customer side to the artist side. This would have the effect of "raising ticket prices" but eliminating fees. Ticketmaster can then advertise they aren't charging customers fees. The reason it is the way it is now is transparency, but it's clear people don't like the dirty details.