But it already has been the case with many businesses that knowing who your customers are is a legal requirement of carrying out transactions with them. For instance, financial, weapons, pharmaceuticals. Restrictions on trade in these industries have been deemed constitutional by SCOTUS, and there isn't any state that doesn't have some restrictions on anonymous commerce between parties
in some cases.
The simpler thing that has happened in pretty much every free country already, is that a government gets to determine what currency tax debts are to be paid in. Furthermore, the state has the capacity to determine that a specific currency must be accepted "for all debts public and private". Having a standard unit of account benefits the society just as other standardizations do, by strengthening network effects.
In a non-failed state with a relatively stable currency there is just no clear path for a different unit of account to overcome these advantages and gain any significant market share (if you have an example I'd love to hear it). Even without legal frameworks enforcing the old order, backwards-compatible marginal improvements to protocols like IPv6 have had weak adoption, because the simplicity and spread of the established protocol makes it good enough. Government supported currencies are even more entrenched.