No, because with classic ID documents, the government doesn't know if I went to a specific healthcare provider, if I opened a social media account, if I bought a train ticket, or even where my bank accounts are (reporting is yearly, not in real time). Accessing all of this data is possible but bears a lot of friction, which prevents mass surveillance (or at least increases the costs).

Once the eID system is set up and becomes ubiquitous, it will be trivial for companies to use eID to open any online account or reserve plane/train tickets. Therefore, giving enforcement forces very convenient access to all of my activity and allowing automated monitoring. Just look at what is happening in China.