This is a pretty common practice overseas, as printing and affixing a destination tag is just part of the self check-in process; however, the law of the land in the United States it that things must be completed by an airline employee.
The thought is that this might speed up the check-in process. Although even if you’re doing stuff yourself there will still be a need to flash your ID and drop your baggage off to go for its ride on the behind-the-scenes airport roller coaster ride.
Seems like a good idea to us, as it should speed things up a little bit. We’ve been frustrated checking in at the airport only to then wait and wait for someone to swing by with a sticker after receiving our boarding passes. The new system is also appealing as maybe we can even swindle an overweight bag onto the plane without getting nailed with an extra fee. Sure the airlines are putting another service into the hands of its passengers, but if you can’t handle something as simple as this you probably shouldn’t be flying in the first place.