Depending on the implementation, I could see that having rate limiting effects. There're only finitely many IDs so scaling sockpuppeting will saturate these IDs quickly but it's quite easy to spin up a new anonymous account. For example, I think the EU ID system has an upcoming way to create pseudo anonymous identifiers that can identify a user per website.

This presents the problem of governments being able to gatekeep speech which I am quite uncomfortable with but maybe there's some safeguard within the eIDAS proposal that makes this idea incorrect?