I believe this is one of those things that's easy to suggest but strangely hard to implement.
The best solution I can think of would be an option to auto-accept the mail containing items or useless information. So you'd get the mail, but they'd be marked as read upon receipt with the items they contain placed in your inventory. You could still leaf through them if you wanted, but you wouldn't have to.
Especially directed towards those that already sell large amounts of items, and even towards small scale merchants (i.e. me and pretty much anyone else to ever use the Auction) this would be a welcome time-saver. However, I would assume that this particular mechanic would only take place offline; a singular, constant message online would be extremely confusing.
It's a quick and innovative fix for a very limited action, making it the perfect step for something of its simplicity.