They absolutely would do both of those things.

A world where Bitcoin was the default currency would rob nations of control over their own monetary policy, which is one of the most important tools for controlling the economy. Not to mention we'd be living in a world of persistent deflation (due to the ceiling on the maximum number of Bitcoins) which would have interesting consequences on the economy too.

The only cryptocurrencies that would be allowed to gain widespread usage would be those controlled by the central banks.

It would only be a deflationary world if Bitcoin were the only currency. Since there are lots of digital currencies, we actually have something like the privately-issued competing currencies advocated by Hayek in The Denationalization of Money.