You'd only be paying the cop to obtain the DNA. You'd still have to pay a geneticist to run the appropriate genetic tests.
Don't be silly. The cops will run genetic tests. And that's not my Big-Brother-Paranoia speaking.
DNA simply isn't useful just sitting in a test tube in some lab... they've got to run genetic tests. Say the LAPD collects DNA from 50,000 people and a crime is committed there. You think the LAPD's solution will be to take a small sample of each of the 50,000 test tubes and compare it to the one collected?
Hah!
Or perhaps you think the police will only run tests on the small sample of the 5 out of 50,000 that could theoretically have committed the crime.
Again I say "Hah!"
That's exactly how people used to compare fingerprints. Now prints are scanned into a computer so that thousands upon thousands of prints can be compared electronically. It's the evolution of information gathering.
Likewise, DNA samples (if collected) will be "scanned" into a computer by categorizing them by a certain subset of genetic sequences. They're going to run some genetic tests. And if they don't look at and record the particular sequence responsible for Sickle Cell Anemia this year you can bet they will ten years from now.