A blockchain is just a database sitting on many computers, which automatically updates itself. One Southern America country is currently looking about storing its land registry on a blockchain. There would be no reward for keeping it, as there is with BTCfor miners, but plenty of attorneys or notaries would be happy to host the land registry of the whole country in their offices.
I am sure everyone would be interested in the ledger itself. But how is the security of transaction validation being managed? One could mandate mining function for all notaries, of course. Take a leap from there... is it safe to say these approaches will have to be closed or permissioned?