[theorique]

But they might feel like distributing the limited cab supply based on luck is more fair than based on who will pay the most.

A similar situation is seen in distribution of immigration visas. Some people 'pay' for the privilege via investor class visas. Some people get in through nepotism via family class visas. Some people get in randomly through visa lotteries.

It's hard to say which of these is more fair than another. Probably depends on your point of view.