The whole thing has been misunderstood by someone and amplified the other way around.

The ban on anonymous payments is on hosted (custodial) wallets, not on self-hosted wallets. It's bad as it is, but it follows the logic of the EU AML, if you provide money transmission services, you must KYC your clients.

I'd be more concerned about the use of CASPs (Crypto Assets Service Providers), an ad hoc made up term that could be easily expanded in the future, at ECB's will, to include whatever they want. CASPs are the ones who need to KYC their clients. For now that's mostly custodial wallets and ecash mints - since exchanges were already required to KYC to operate in the EU. In the future, they could use this term to include LSPs, lighting nodes, whirlpool/coinjoin coordinators, robosats coordinators, whole L2s like liquid, etc...