The main benefit of Proxy Bidding is that you do not have to sit at your computer for the duration of the auction, continuously outbidding your competition. Another benefit is that Proxy Bidding helps prevent Buyer's Remorse. If you only bid once on an item, and carefully decide how much you want to bid, then are you are less likely to end up spending more than you are willing to, or can afford. This doesn't always work, though. That's where sniping comes in, but in general if you steel yourself to Proxy Bid only once, then such problems are minimized.
Proxy bidding puts the minds of non-winners at ease, sort of.
If you Proxy Bid correctly, and still lose, you will know that the person who won fairly and squarely outbid you and was willing to pay more than you were. It's stil disappointing, naturally. I've lost before, and I can't honestly say that I was overjoyed, but it's better than nothing. It would have been worse to know that I would have bid more than I did, perhaps beating the winner if I had bid correctly in the first place. Finally, the proxy system is self-running.