That is not where trust in the dollar comes from.
It comes from stability. Predictability.
Courts and law enforcement certainly provide these things, but they are not required. The inherent design of blockchains makes them trustworthy (an oversimplified statement), which is even better.
Blockchains don’t, and can’t, solve for the risk of the off chain component of an exchange.
The transactions aren’t atomic so someone is taking on counterparty risk. One of governments prime responsibilities is dealing with that risk, no matter the currency in question.