Banks and governments buying BTC may never be a world wide thing, there may be some governments that would hoard BTC for their own reasons we may never know of, but that number will be very small and of little importance. Think of it, with the problem of inflation and other critical economic problems plaguing many nations, most of them living in poverty and can't provide anything for their citizens, buying BTC should almost be off the cards for them.
Currently most nations especially in developing nation are sustaining their economy by through borrowing. The global economic crisis have made most government to focus on how to run their nation and investing in cryptocurrencies would be a minor option. Also, the volatility of bitcoin would discourage most ignorant government from investing in bitcoin. Most government official have little or no knowledge about the operations and opportunities of bitcoin investment.
Another major challenge that would discourage most nations from investing in bitcoin in the developing world especially Africa is colonial influence. Most nations in Africa depend financially on the World Bank and their colonial masters. They must consult these financial institutions before they make any investment, failure to do that might lead to severe financial consequences. So most nations are scared that they might not access more loans or receive a loan payment adjustment. Countries like El Salvador and Central African Republic boldly adopted bitcoin regardless of the pressures and opposition of most global financial organization.
As long as they cannot control bitcoin, it would not be a bad idea if banks and government of nations invest in bitcoin. It would affect the price positively and it could also lead to massive adoption of bitcoin in those nations.