"Should" - based on what legal or even rational basis? Or just your personal and subjective "feelings"?
• They've got a serious crime, like a serial killer, but no real suspects. They do have some DNA that is almost certainly from the criminal but it does not match any DNA they have on file.
• Years later they compare that DNA to DNA in some large DNA database that is not focused on criminals.
• There are no matches that indicate that the criminal's DNA is in that database, but there are several matches that indicate people who are relatives of the criminal.
• They can then look at assorted public records to find people who are related in the right way to some of those relatives.
• Among those people, some previous person who either never was a suspect originally or a very weak suspect comes up. They then take a thorough look at any records can find about that person's activities at the times of the crime and find that they were actually connected to most of the victims and in the right places at the right times to be the criminal.
• That gives them enough evidence to compel a DNA sample from that person, or they start watching the person and get a DNA sample from something like a discarded napkin or cup that the person unwisely discarded in a public trashcan. That sample matches the samples from the crime scene.
• It is that latter sample, and the records of the person's activities and relationships with the victims, that form the bases of the conviction.
https://www.nytimes.com/2018/10/15/science/gedmatch-genealog...