Isn it true that if ticket brokers didn buy up tickets there would be plenty of seats for all the fans?
Not at all. Ticket brokers generally only have a very small amount of tickets for any concert and it does not affect availability at all. Most shows that are sold out would not even come close to having enough capacity for all fans to attend. You may see many brokers advertising many tickets for the same concert, but bear in mind that the ticket network is wide and most brokers will source at least some of their tickets from other brokers.