Governments might not do this, because by doing this, they would admit to their own failure to protect their own financial economy and reserve currency.
That's not necessarily true. Look at the Chinese government stockpiling gold. All major governments have gold reserves, even if it has no relation to the value of fiat money. Governments necessarily diversify to hedge national/government assets against economic turmoil and inflation.
I don't see central banks advocating for it, though.