This feature dates back many years to when full IDs were shown. It allowed buyers of embarrassing items to hide their purchases.
Now all IDs just show as a***b for example, soprivate auctions are not really needed.
Unfortunately some Private Sellers think they have to use them, BUT it is also abused by other sellers to hide shill bidding.
Shill bidding is very difficult to prove but by using a Private Listing even the suspicious signs in bidding history are hidden. Many buyers will avoid Private Auctions, or if bidding bid only once or as late in the auction as possible.
