As far as I am aware, the eIDAS or whatever those bureaucratic names are, is DID - Decentralised Identity. Normally this would mean that user has full control over their credentials. This could lead to only government trying to overuse the identification on many government services.

What I am not sure, though, is which blockchain this DID is anchored at. I think the EU has some private one. So this might mean they can cancel you in anytime.

Also Issuers would have too much knowledge maybe. And Verifiers might talk to each other secretly that this or that DID did identification.

I think one of the cases that was shown as quite risky was charging your EV, using your identity to different charging stations could track your movement quite successfully.

Regarding the ZKP Credentials - they might Issue Atomic credentials and still get the same control over facts, but there are much more benefits than what was described in the article to support ZKP.