I don't understand why the solution, at least in PAX's case, is not to ban bots. That would open up purchasing to regular human users, and since PAX is a ridiculously popular event, tickets would still sell out.
Yeah, pretty much this. PAX is a huge, widely popular event. It has an entire community built around it. I suspect that the vast majority of people would not mind filling in a captcha if it means they will have a much better chance of hanging out with friends they made in previous years' PAXs.
PS: your answer isn't allowed to be captcha.