Maybe the way to solve this issue is for law enforcement to be required to mail a letter to everyone who is in the database that they are a suspect in whatever crime being investigated each time law enforcement executed or delegates the execution of a search query. I mean that is how search works: you search everything or you compute hash functions on everything to avoid searching everything, but you’ve effectively tested whether or not everyone in the database is the suspect.
On a slightly different topic, how well are these DNA databases secured and maintained? A person’s DNA might not change, but the corresponding entry in the DNA database is subject to theft, manipulation, and data corruption. What’s stopping the presumption of innocence until proven guilty becoming the presumption of innocence until the DNA database reports a match? Arguably, people should treat DNA databases with the same level of suspicion and concern as some view electronic voting: absolutely vulnerable and absolutely abusable until repeatedly proven to be not sufficiently many times.