Sniping has always puzzled me. What you are describing is exactly what proxy bidding does anyway - how does sniping help?
No, it isn't, in a couple of subtle but important ways. (For the moment, I'd also pass along this as a reference as well)
The problem with proxy bidding is it still encourages "nibbling", as it will continue to make bids on your part, in small increments, every time a bid comes in that is over your current proxy. This encourages traffic, and emotional bidders, and the end result may - and often is - a higher cost to whomever eventually wins the auction. With a snipe, I still set a maximum that I wish to pay, and I've grown very comfortable setting a maximum and living with it if someone outbids me! However, the bid doesn't get placed until some (short) amount of time just before close. My bid will never artificially drive up the price, and I still don't have to be online to take care of the bidding when the close of auction occurs.
There are other features that some of the snipe services have. One I have used, though infrequently, is grouped bidding (there may be other names). If, for instance, I see an item that appears from multiple sellers but might be ending at similar times, I can set a snipe for these but group the bids; if I win the first-closing auction, it cancels the other bids; if I don't, it continues on, etc. This ensures that I might be able to purchase a particular item (oh, say, three different people have similar Sheaffer OS Balances for sale...), but I never end up buying more than one of them. Rare situation, but handy if you need it.
Not to mention that sniping programs keep all my bidding in one place, where I can review progress and alter or delete bids easily from one interface, just a bit less work than on the eBay pages proper.