I agree with some of your points, except that the initial absence of probable cause makes this case worthwhile.
The reason to defend constitutional rights in this context is about what the government 'could' do, not what they 'should' do. As an example, I think very few people would argue about the plausible deniability of a person found with a dead body in their trunk and yet there are cases arguing about whether or not similar 'evidence' should be considered if it was discovered due to a traffic stop without cause or an improperly served search warrant, etc. The reason is not because constitutional rights advocates want the possibly guilty to go free and not because we don't want law enforcement to be able to do their jobs, but because we don't want abuses to become the norm rather than the exception.
If the courts decide that the DNA of an individual can be tested without a warrant or even probable cause, then they could just begin testing everyone that had even passing contact with a victim, a neighborhood street, a school, an entire city.
At the most extreme, the FBI could then begin to secretly collect our DNA when we go to any federal office and eventually have an entire database they can search for a match to any random DNA found at a crime scene. You might try to compare this to fingerprint databases, but those are databases of people where they was legal cause to require collection of their prints--convicted criminals and law enforcement officials are two examples. And remember that neither fingerprints nor DNA are definitive; labs make mistakes, samples are mishandled, etc.
If there was no fear that evidence could be thrown out because of how it was collected, then law enforcement would just proceed unhindered in any investigation and worry about consequences later when they got their arrest.