Here's a simple one: do we really trust a government agency (or hell, anyone really) to collect intimate and identifiable data about our bodies all while preserving anonymity and securing the data from nation state attackers? Do we trust nameless data scientists to run SQL queries over us that aren't intended to determine which ones of us will be smarter, stronger, more violent, etc? Do we trust politicians that have not yet been elected to office to use this data for benevolent purposes like our current politicians would (if we trust our current politicians)?

Maybe there is some benefit to running such a program, but it would be outweighed by the vulgar distrust that would fester inside of concerned populations and spread to non-controversial parts of the government such as the post office and the voting process. Concerned populations here are not just conspiracy nuts; it would include undocumented immigrants, Black and Hispanic minorities, and probably a good chunk of Jews.