Under such a system - how do you know that there is anything behind the government's numbers? They could be pure fiction right now and no one but the government would know. Also, the government takes a cut. As the whole economy flows through their currency, they become a de jure taxing body. Their taxes drain the economy, and can be used to manipulate the economy to the government's whim.

It may shock you to learn that not everybody trusts the U.S. government. The growth of cryptocurrencies worldwide is largely fueled by the fact that the set of people who don't trust the U.S. government is larger than the set of people who do - and in fact, they've seen their biggest up-take in societies like Zimbabwe and Venezuela where trust in civil monetary authority has completely collapsed.