Fiat cash is centralized and handily constrained by banks and governments.
Where bitcoin is decentralized, so it is implausible for bitcoin to support up US Dollars.
There's no correlation between bitcoin with fiat. Both have various highlights and characteristics.
But mostly it is because it is a cryptocurrency with a high volatility rate, as opposed to USD which is a fiat currency with regulations left and right.
The main thing government can do is improve the stock exchange and its economy.
It can be backing up the dollars; there are no rights for bitcoin to do anything with fiat in any case.