The more this signature is necessary the harder it becomes to deny issueing it to somebody.
I don't see how this changes much compared to nowadays. You can already require an ID for all kinds of these and the government already has total control over those. So what changes? China manages to ruin the lives of the people illegally born under the 1-child-policy for decades already, all without systems like eIDAS.
You can't protect yourself from authoritarian regimes with tech or good policy since those will just get ignored. Look at Trumps war with Iran, where did Congress agree to it?
I'm not a fan of these systems either, I also think software should be open and no vendor lock-in should exist. But I don't think this will change much to be honest.