"Do you mean you don't think people can be trusted to keep their own shares safe?" Well, to a degree, yeah. Most people don't know how to properly keep them safe.

The main thing I'm trying to say is that it's potentially easier to steal shares, and there is really no way of reversing it if it's decentralized. If you know some shares are stolen, can you invalidate them, or reissue shares? It's not really completely decentralized if you can. There is probably still a central authority for creating and issuing shares, but they will allow you to trade the shares in a peer-to-peer way.