It's not even about reputation, it's mostly about taxes. You enforce the private sector using the state's monopoly of violence to pay tributes in a currency that you create. This way, when there are transactions in the private sector, the main currency that people will want to use (provided it's stable enough) is the one that lets them pay their taxes later. You can't pay taxes with dollars in Hungary, which makes Hungarian people use Hungarian currency instead of Chinese Yuan even if the Chinese Yuan is a much stronger currency.

And yes, the state having the monopoly of violence and enforcing taxes is a good thing, before anyone accuses me of being an anarchocapitalist.