Financial anonymity not the same as data privacy
Messages containing money are not the same as other messages in relation to privacy law for tax reasons, and the responsibility we give governments to combat organised and international crime, which is the primary legitimation for governments to exist. Cash is an acceptable risk for governments, in the sense they get the seigniorage which is a form of tax, there is little alternative to this existing, and holdings of large amounts can be stopped and searched under warrant.
The complex way for governments to combat use of cryptocurrency for money laundering is to publish a real time database of tainted wallet addresses, to taint each wallet these pay into, and to treat every owner of a tainted wallet as a money laundering criminal accessory, with a fine of a multiple greater than one of the tainted part of their wallet. All the data needed is in the blockchain, combined with a record of criminal complaints received identifying offending wallet addresses.
The simple way is to close down all the cash for crypto exchanges as money laundering accessories.
The tax and money laundering issue isn't the same as whether governments can or should have the power to prevent use of or break into strong encryption other than at endpoints. That ship sailed long ago.