A census counts people. It might need to know who's a citizen or who's eligible to vote, or maybe even generation or sex. It doesn't need to know name, address, eye color, medical history, fingerprint, etc. The aggregation provides privacy (unless the sample size is incredibly small, like in an extremely remote district).

Another example is the TSA: their job is to protect vehicles and passengers, which means preventing weapons on airplanes. But it doesn't matter who's wielding the weapons. So they don't need ID to do their job, and asking for it (and worse, recording it where it can be leaked) is an unnecessary breach of privacy.

The general problem is there are incentives for collecting excessive information and very few disincentives. Laws and regulation can change that.