I am carrying an ID card - as I am obliged to carry it here in Germany (or a passport) -, and I have to use it quite rarely.

Mostly when flying to other countries (I could use a passport instead, but why bother to get a passport when I have an ID card anyway) or when I collect parcels at the post office when I was at work while they tried to deliver them.
Then of course I use it at the election office.

Post office is a private company, so no chance for the government to collect data (or just the same amount if I used a different way of identifying myself).
At the airport, the government would get the data from a passport as well.
At the elections, I could prove myself being me with a passport as well (independent of the means of identification, the govenment could collect the data [i.e. that I went to the election] from the tick made in the electors' list).

So I don't see how the government could collect more data because I carry an ID card compared to when I would not.

I have never been asked to show my ID card just because a police officer wanted to see it - whenever I used it, I could have used a passport instead...