I worked for Ticketmaster as an Engineering Director for a few years. Reading through the comments, most of them are wrong. Here are the real reasons, imho.
(1) The ticketing system you want as a consumer is not the ticketing system that artists/venues/promoters want. As a consumer, you hate those Ticketmaster fees. The others? They love those fees. That's how they get paid. There are almost no standard fees for Ticketmaster. Every fee is contract specific and split between the parties. From the convenience fee to the print-at-home-free -- cuts of those got to everyone.
You could build the consumer-friendly platform, but it's not going to be used anyone, and certainly not by top artists. Top artists expect to get get 95% to 105% of the ticket price (yes, more than 100%). That leaves everyone else (including the promoter & venues reliant on other revenue streams like fees.
(2) The business requirements make it a technical beast to solve. Nevermind your LAMP-based ecomm site. Tickets aren't fungible. That creates a lot of problems. Thing selling airline tickets, not widgets on Amazon. Venues can be configured in countless ways. Pricing strategies are complex, often unique per show & dynamic. Most shows don't sell out. The promoter is the one who took the financial risk and needs to figure out how to maximize the revenue per show. Once the show is over, those unsold tickets are worthless.
(3) Scaling is hard. Massive spikes during onsale, but very low QPS at other times. The hardware cost profile is challenging than most non-FAANG services.
(4) Creating a ticket system for a small theatre with fixed seating, or purely GA events isn't that hard. What's hard is a top tier artist going on tour across the country. (And that's where most of the profit is.)
(5) Ticketing isn't that profitable. You'd have to invest a lot of resource for not much gain. The last serious attempt was LiveNation. They dumped hundreds of millions trying to build their own platform. Then gave up & bought Ticketmaster.