The thing I find most interesting about governments is that there are so many that complain about the inefficiencies, surveillance and corruption but when faced with legal issues out of their control such as theft of their personal property or large scale fraud (Mt. Gox) that they would turn to their governments and demand that they solve the issues. The US Government in general is horribly inefficient with Democrats and Republicans spending all their time arguing over issues that nothing really gets done and hundreds of millions of dollars are spent every year in order to make the other side seem less credible along with over bloated pension funds and exuberant wages for basically doing nothing when that money would be better spent on basic needs. The Blockchain solves a lot of these issues by taking away the centralized control of the monetary system but the first thing that comes to mind when thinking about the adaption of the Blockchain into a full nationwide monetary system is how Governments would pay for maintenance of infrastructure since it isn't like the average person would just go out and donate money to the Government in order to pay for these services. It seems inevitable that Governments would have to transition to Blockchain technology and the sooner they start to adapt the better but they have yet to even begin and the question would be, how they would make the transition?
The only reason we have governments is because no one can stand the alternative. (That would be organized crime, but I repeat myself.)
I believe that the way forward is to provide better alternatives to government, things that make government irrelevant, things that restrict its abuses, but not the elimination of all that is barely keeping a finger in the dike of untamed human nature.
Anything that will work on the blockchain shouldn't need government - let the free market handle it. Bitcoin funds itself via inflation at the tune of several hundred million dollars per year. At government replacement scale, that would be many billions available to fund operations. Um, if you didn't have to burn it paying miners to buy electricity.
At government scale using BitShare's DPOS "miners", all those funds would be redirected to pay for useful work like operations, infrastructure, and developing new services.
Of course, with BitShares we are only recycling a few percent of annual growth to fund growth. Long before we reach government scale, we won't need to do that because we can fund it all out of fees for services rendered. So far to date we have been net deflationary.
So, yes, move as much as possible of what the governments do onto the block chain. That's ultimately what we are trying to do to wean ourselves away from dependency on government to enforce a level playing field and an incorruptible set of rules. Providing a decentralized exchange and stabilized currency products is just our warm-up act.