It's starting to happen. Not that Bitcoin is totally replacing fiat, but at least Bitcoin is now a legal tender in a couple of countries. Some others might follow. But the influx will probably happen once the current monetary joke will be made obvious and the paradigm shifts. Who knows, I'm hoping the next kind of money will be detached from the powers of the state and totally free from abuses. Bitcoin is a good candidate. This might happen in the next several decades, though, or not at all.

You don't have to worry about Bitcoin. Governments can't kill it. And the wider the adoption grows, the harder it is to even try shutting down.