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The purpose is to make supply closer match demand. If fares increase, more drivers will be willing to drive. If fares increase, less consumers will request rides.

You're correct in assuming that increased prices will reduce the number of drivers demanded. But you're wrong in assuming that the pool of available drivers remains static when prices increase.

An increase in price both reduces the quantity demanded, and increases the quantity supplied. I've personally met Uber drivers who plan their work schedules around the times when surge is highest.

I think you are missing the part where drivers get paid more during surge pricing. An increased reward entices more drivers to come out during that time.

Or motivation for drivers to deadhead to a surge area, or take a couple extra rides before taking a break/signing off the for the night.