https://en.wikipedia.org/wiki/Edward_Snowden#Revelations
The existence of eIDAS itself is already a big problem. They're going to try to gradually push laws to make it so that you'll need a government issued signature to do anything. That's when they'll have total power over you because they can simply refuse to issue.
Modern computing and communications technologies can be leveraged to build infinitely stable authoritarian regimes. It's even possible for democracies to stumble into it on their own as they attempt to regulate these new technologies. In hindsight, the Internet was built wrong. It has a top-down structure which all of human civilization is beginning to mirror.