"For a moment he felt good about this. A moment or two later he felt bad about feeling good about it. Then he felt good about feeling bad about feeling good about it and, satisfied, drove on into the night."
-- Hitchhiker's Guide to the Galaxy --
At one point I was able to run a PGO shotgun accurately and fast. This was due to me receiving bad advice and getting a great deal on a PGO 500, as well as being young. Pretty much the same reasons I spent a lot of time learning to point shoot.
It can be done, in the same way you can make a great pool shot without looking down the cue. Know what it takes to do that? Shooting a LOT of pool. Know what it takes to be accurate with a PGO shotgun? Shooting a LOT of PGO shotgun. That training time can be way, way better spent, considering the few advantages of a PGO shotgun, which in my experience are:
1. It's shorter. If this is that important to you a tax stamp will be much cheaper than the time/ammo spent training.
2. It's somewhat handier in tight/confined/awkward places such as vehicles. This is very relative and depends on a lot of factors. Again, training.
3. It's somewhat easier to stay peripherally aware. Training to do this with a standard weapon takes less time than learning to shoot sightless.
4. For some reason it looks intimidating/scary to people who lack firearms knowledge/training.
5. Somebody wrote a catchy song about it.
As opposed to the disadvantages which include:
1. With a LOT of practice, it's possible to make an accurate long range slug shot, but I was never able to figure out a way to make a reasonably fast follow up
2. Firearms have sights for a reason.