If, and it's a big if, the gov't can come up with a crypto that is easily moved around the world without the need for a trusted third party, there won't be a need BTC.
If a gov't backed crypto can be had by the rank and file of all the third world countries, easily moved across borders and used peer to peer as a medium of exchange, is there really a need for BTC.
A US dollar, Euro or even a Gold backed crypto would fulfill most of the need in the unbankable world. Where then is the value of bitcoin? All I can see is rarity and the hope there will be someone who will pay a higher price than you did.