I would love to 'own' all my data. But companies offering services will win out because they do not have to play nice with you or your data store. Take Gmail, Facebook or Google docs as examples. In principle that's
your data. But Gmail has successfully convinced people that Google is able to run its mail service better than you or your corporation ever could. In return for 'reading your mail', and vast amounts of corporations and individuals seem to believe them.
Ditto for Facebook and yet another encore for Google docs.
Once established economies of scale and network effects will do the rest. A new system would have to fix a lot more than just the security angle because it is well known that security is always going to be secondary to convenience, a factor that large entities will find much easier to control than many small ones.
So, I really hope they will manage but I'm not going to hold my breath until they do. Note this comes from a guy that does not have a Facebook account, no smartphone, runs his own web and mail server.