Car registrations are required. You are allowed a choice of owning a vehicle knowing what it requires. Sample of your DNA and fingerprints is not a requirement when we are born.
Thus I find the comparison not adequate.
But it wasn’t the suspect’s DNA it was his relative’s. Deleting your own information would not be a sufficient privacy measure in this case. It’s increasingly statistically likely that someone you’re a relative of will be in a DNA database, it’s simply not tractable to ask all of them to remove their DNA. And what about when some of these people die, can I take down my late grandma’s DNA.
So to tune the analogy: "A white van was found at the scene. Police have reason to believe the van's owner wasn't driving that day and investigate the owner's son, who is also known to sometimes use that van. That investigation reveals much stronger evidence that the son is the perpetrator."
I see no issues with this chain of investigation. Some tools the police have access to you cannot personally opt out of. That's working as intended.
If I am European and I ask Facebook to remove my data, will they also remove pictures of me which are owned by my family? I doubt it, and that's also the problem with providing consent on these DNA databases - they don't require the consent of all of your relatives.
Lets assume that instead of DNA evidence, they had a photo of a white van at the scene of the crime.
In that case it would be obvious that the police would search databases for people who own that model of car.
If police would need to have a specific suspect in mind before they start investigations, how would they ever be able to investigate anything?