It’s because people are significantly more likely to lie or omit some facts if you don’t guarantee their privacy, which means your census data ends up being worth less than a pile of shit.

The alternative is to water down the census questions, which also leads you down the same path (i.e. manure as data).

How about we should be "counting illegals" so that we know how many of them there are?

(Do you reject that? As someone who uses the phrase "counting illegals" I imagine you would be interested in knowing what that number is.)