It is not the job of "base money" to be stable against other currencies. Base monet doesn't give a f*ck
people don't need to use it - they have a choice and they will go to something less volatile. Trading one volatile thing for an even more volatile thing is madness. People don't like that concept.
Bitcoin as basemoney can't compete in the long run due to its volatility. Yes, it is the job of the basemoney to be stable if you like it or not.