What you’re proposing works only if the government is always trustworthy and abiding by the rules. But there has been cases that ICE agents in US was able to track down people from their social media posts and in the past Nazis used the address registration lists to track down Jews for deportation to concentration camps.

We don’t know what EU would become in 5 to 10 years in the future, and I would rather not have any identification information about me or family being stored by a government body or any other party that can track/link me or my family members