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).
So you seem to have at least a surface level of understanding of incentives.
Check this then:
If the census is responsible for allocating federal funds and congressional apportionment, what are the incentives for making census data private and encouraging people that would otherwise hide their identity?