And it's well-known since early eBay days that many bidders are irrational, including but not limited to competitive impulse to "win". Plus you sometimes have shill bidders.
Sniping approximates sealed bids, with the highest-bidder the second-highest sealed bid amount or a small increment above it. (Unfortunately for eBay, that would tend to decrease their cuts, unless the appeal of the sealed bid format brings in sufficiently more bidder activity.)
Another advantage of the software/service is that it automates. If you want to buy a Foo, you can look at the search lists, find a few Foos (possibly of varying value in the details), say how much you'll pay for each one, and let the software attempt to buy each one by its auction end until it's bought one, then it stops. If eBay implemented this itself, it might be too much headache in customer support, but third-parties could provide it to power users.
(I don't buy enough on eBay anymore to bother with anything other than conventional manual bids, but I see the appeal of automation.)