When supply isn't constrained, auctions benefit everyone. Not just the 'wealthy minority'. If we fixed airline tickets at $400 each and apportioned them lottery style we are ignoring that many business travelers would happily pay $600 for a certainty of getting a ticket and people of limited means would gladly trade time/travel flexibility for a $200 ticket.
Similar forces are at play with taxis. If you line up everyone waiting for a fixed number of taxis at a fixed price, you are ignoring that many people would pay more to skip the line. Paying more will increase the total number of available cars. Shortening the wait time for everyone.
People look at variable pricing as a way for 'rich people to get everything' when it's really about letting some people pay more to subsidize others who pay less.