The problem is, with a limited supply of tickets you’re going to draw the line somehow whether you want it or not. Price sets the barrier explicitly. Attempts to avoid using that (e.g. in various social welfare programs all over the world, but also throughout the late Soviet consumer economy) have usually ended up instituting a different, implicit barrier that may seem less outrageous on the surface but at the end of the day is not that much better: networking or bribery skills, amount of time to spend standing in queue or refreshing the website (frequently turned back into price by various enterprising people—I wonder if the US Consulate in Moscow realizes the reduction in visa interview capacity a couple of years ago had as its main effect funnelling applicants’ money to a small, untaxed, and technically illegal industry of bot programmers).
If you’re trying to extract as much money from each customer as possible (as airlines and other “discriminating monopolies” do), those additional barriers might be intentional. Otherwise they don’t seem that much better than the original money one—I guess you could claim the most passionate fans will be able to buy cheap tickets that are sold out in hours (one possible barrier) but you’re automatically cutting off people who can’t afford the necessary time off work to monitor the sale as well, for example.
I don’t like this. But I don’t see a workable economic mechanism that can do substantially better, either.