They have tried a bunch of methods like demand based pricing, ID verification, electronic tickets, and lotteries. I suspect these things only work a little and each has its own problem side-effects.
Bands with the clout and fans lined up down the block the day before ticket sales open (e.g. Radiohead, The Cure, Pearl Jam) can do these things, and I'm glad they do. For the vast majority of acts– even well-known ones– it's absolutely not an option.
I think pretty much any act popular enough to headline at a large LiveNation venue can do this. Not even all that is necessary: just ID verification. Require each ticket to be associated with a real person's name at the time of purchase (and the ticketing platform should make it easier for people to find tickets next to or at least near their friends when they have to buy in separate orders).
Tickets aren't transferable. Ticket purchasing platform has a marketplace where people can resell tickets to others if they can't attend, and sale price is capped at whatever they paid in the first place. (Or the ticket issuers can partner with something that already exists, like StubHub, and contractually require the price caps.)
Each attendee must present their ID to enter the event. Names must match, no exceptions. I don't love the idea that you can't anonymously attend a concert (by walking up to the ticket counter and paying in cash, assuming any large venues even have box offices anymore), but I think the benefits of this scheme for the majority of purchasers far outweigh that negative.
This isn't hard. It's almost as if someone in the chain likes scalpers...
Indeed, the problem would not be difficult for LiveNation to solve.
Those acts are still the minority of things they book. Within maybe 30 miles of where I live, there are probably 15 big venues that house huge acts like that, but hundreds of smaller clubs, event spaces, halls, theaters, etc that use LiveNation. I used to work at a bouncer at a little rock club with like a 250 person capacity and they used them for ticketing.