Bitcoin solves the issue of trust. Bitocin itself will never work as a currency that governments can rely.
First reason for that is that governments want control over their money. There has to be a central authority for multiple reasons. Banks need bailing out? As much as I'm against bail-out, sometimes the damage of not bailing them can be far greater than not bailing them out. Need the £85k insurance that your money is safe in any bank?
Governments need control of their own currency. Bitcoin does not provide that.
I see Bitcoin more as a commodity. Something like gold, and just like gold, the supply must be finite. This is something Bitcoin provides.
There is nothing stopping a government from building their own cryptocurrency that they'll have control over, but that gets rid of the main selling point of Bitcoin, that is that you don't have to trust individuals (for the most part anyway).