I think the federal reserve is too close to the status quo to be effective for this. It is owned by the federally chartered banks, the same ones that all have longstanding relationships with the current payment processors.

A government organization like the mint should be in charge of the layer 1 of money transfer. Let the current providers adapt and sell their other services on top of it. It could be crypto, copy the existing systems, or be something new all together. It doesn't even have to be free, they could add in a small transfer tax or whatever. The point is that any person or business should be able to send money to any other, for any reason. At the very least within the country.