Governments can print money, so if they want bitcoins it would be much more efficient for them to just buy them (with newly printed money) than try to mine them.
Going on a bit of a tangent:
Once common criticism of bitcoin is that there is nobody like the Federal Reserve to "smooth out the bumps in the economy by manipulating the money supply." Set aside for a minute whether or not the Fed actually does a good job of that or whether or not the Fed actually has the ability to do that.
One response is that there is absolutely nothing stopping the Federal Reserve, or anybody else, from stepping in and "smoothing out the bumps in the bitcoin economy." The Fed could buy bitcoins when it thought the value was too low, and sell them when it thought the value was too high. It'd have to plan ahead and keep a big stock on hand so it had some to sell, of course.
That might lead to a productive discussion on why that would or wouldn't work, and if or how it is different from what the Fed (or the World Bank) does now.