My '63 Bambi had one, but the compressor was dead, so I removed it. The tank was pretty small and heavy, so a larger plastic one gave me more capacity, along with lower weight. The air pressure system would work about the same as any home well system with an air over water, only as the water is drawn out of the tank, the compressor would come on to replenish it with air, keeping the water pressure up. The compressor, like a demand pump, is noisy, however you could shut it off overnight so you were not having it run then, only the residual air pressure would push the water out of the tank. The tank fill cap has to be sealed without leaks, and you need some way to relieve the air pressure prior to removing the cap, otherwise it would blow off in your hand.
I can think of no real reason to keep the compressor system, other than the ability to have water without noise overnight. Time and technology has marched on I think.