[derefr]

The thing is, in the case where arbitrage doesn't exist, people without discretionary income still lose—because people with discretionary income can trade that income for someone else's time, which they can use to reserve more slots in any sort of a non-monetarily-determined distribution system (paying them to stand in line for them to get a first-come-first-served finite good; paying them to enter a raffle for them; etc.)

Adding arbitrage just makes this process more efficient, by allowing the richer consumers to express their desires directly, rather than having to hire someone (or, more likely, pay a service to hire someone, or use someone they already retain for miscellaneous tasks) to spend their time (exchanged for money) to acquire the good. Either way, richer consumers will preferentially acquire goods in a market; that's one of the fundamental properties of markets, and can't really be divorced from them.