Perhaps the best "big name" distrusted CA would be Symantec: https://blog.mozilla.org/security/2018/03/12/distrust-symant...
Others include WoSign and StartCom.
The problem with eIDAS is that browsers can no longer police these CAs, as they are legally mandated to carry them. There needs to be a mechanism whereby such a CA can be distrusted, doubly so if it is issuing "qualified" certificates (if it cannot get the basics right it should not attest to someone's legal identity).
On the flip side to this there is nothing stopping Europe distributing additional roots that install themselves in browsers. I work in finance and we operate several closed CAs. Our clients install our CAs all the time. It just would not be on by default nor pop up the EV bit.
But that does not stop the digital wallet software (the motivation for this) peering into the certificate itself and making sure it is a qualified certificate.