Changing stock trading protocols to go on a block chain with full public transparency would be a useful application. No need for PoW, you can just have the Fed mint new blocks out. This would prevent a lot of the shenanigans and gatekeeping that occur in capital markets. It would greatly improve price discovery.
On a less directly applicable level, I feel that the only realistic strategy for governments in the long term will be to become more competitive with the crypto-ecosystem (currencies, contracts, encryption, etc.). The hope being that by allowing individuals to freely choose their own legal and financial rule-sets the systems that will remain relevant will become better. Having more freedom of choice for which government you'd like to be a part of is ultimately a good thing. Whether that will actually shake out is anyone's guess, but I believe something along those lines is the fundamental hope of this area of technology.