Obviously it wouldn't be anonymous. It might not be able to be international. But liberal Western governments want their citizens to be able to interact economically with each other easily (but taxed), don't they?
I recall some messaging from the EU about their interest in establishing ways for ecommerce to work over the continent, without relying on foreign credit card companies.
I guess I should read up on the history of failed microtransaction systems.
So anyway, it's arguable that no anonymous digital money system can remain law-abiding. And if it's centralized, it will be taken down.
Bitcoin isn't anonymous. But for small amounts, it can be effectively anonymized. However, it's very hard to anonymize large transactions. It's the "snake eating a pig" issue. So maybe that's why governments cut it some slack. Punters have decent anonymity, but hardcore money laundering is unworkable.
And to actually address your question, I gather that many digital money systems are in development, which are designed to be strongly non-anonymous and law-abiding. But it's a hard problem, without ungameable online identity authentication.
Centralization enabled government take-down :(