They do. It's called "Quantitative Easing" or "Liquidity Injections". The EU has been doing this for the past few years in hopes of getting inflation above 0. When the state prints money, things get more expensive. That carton of milk that used to be 1.50 euro is now 1.75 euro. More money in circulation means it's less valuable.

The idea behind limiting bitcoin was to prevent it becoming a victim of inflation, like other commodities. But banks has a solution to that. It's called "Futures contracts". They allow huge speculators to bet their hyperinflated currency against a commodity, and it loses value. If bitcoin can be centrally regulated, this will happen.