The point of a warrant is that a judge has decided that the needs of law enforcement override the right to privacy in this case. The point of the lawsuit is to set a precedent saying that the police cannot simply collect and analyze DNA without warrants.
Therefore if there is a demonstrable privacy issue to DNA collection and analysis, then requiring warrants is the accepted way in our legal system to balance the needs of law enforcement against people's right to privacy.
I think this is also a stretch. Fingerprint databases have existed for quite some time, and yet police are not required to get a warrant to check finger prints collected from a recovered weapon against that database, which can reveal quite a lot about the history of the person.
Fingerprints cannot tell you who a person is related to, or about their likely medical conditions. DNA can. (Though the limited set of markers used in police databases can't. But they also misuse those markers and overestimate the odds of a match. However that is a different and more complicated issue.)
Therefore if there is a demonstrable privacy issue to DNA collection and analysis, then requiring warrants is the accepted way in our legal system to balance the needs of law enforcement against people's right to privacy.