Parabon, the company that helped catch Golden State, used a different (yet similar) technology to what you’re describing.
Those states use databases of criminals that have their DNA on file, in order to generate a familial match.
Parabon’s process uses a site called GED Match, which is a public database.
People upload their results from Ancestry and sites like it, to this public site.
Parabon uses this information to generate a family tree, one that leads to a probable suspect.
Law enforcement takes it from there.
As far as I am aware, this is legal in all states, as it doesn’t use criminal databases.
Good synopsis.
LE then go further, and look at known addresses, birth/death records, marriage records, adoption records, cemetery records, etc. Det. Holis that was involved in the GSK case for many years, mentioned that they were literally walking through cemeteries to try and find familial links.
It takes time when they get workable DNA of a suspect, I think with GSK once they linked him to a third cousin through one of those ancestry sites, it took 4 months of gumshoe detective work to find him.
I have to stress that the linking of DNA through ancestry sites, and forensic genealogy resources, is a new method. Meaning under two or maybe three years. My take on more recent cases is the collaboration and cooperation between the FBI and various agencies, and genealogy experts, appears to be speeding things up a bit. A recent 40+ y/o case was solved in a matter of weeks, but it looks like it takes some months to bring things to the point where they can get a warrant for DNA, for most of these cases.
It's an extremely laborious and tedious process, much of the ancestry stuff they go by cannot be found in searchable databases. GSK was found through a 3rd cousin. That third cousin could be in Europe, for all we know, in fact IIRC the genetic link in that case was traced to an ancestor from the 1800's. So imagine sifting through not only non-searchable records and databases, where you have to scroll through online records/web pages from the Geocities days (I've done it myself), but you have newspaper records, church records, cemeteries you have to walk through to find dead people, census records, etc. It takes time, unlike a one hour episode of a fictional TV show.
I'll use my own maternal mother's side as an example. The genealogy for that family from western Ireland took me down what I thought were rabbit holes and dead-ends, when in reality there was a name change about 100 years ago. Their last name was changed, and there's no explanation for it, and nobody in the family ever brought it up. Yet cousins of theirs across several countries across the globe did the same thing, changed their name from one to the other, and the two names are very close in spelling. That would frustrate genealogy folks and investigators, but eventually records became more concrete and easier to follow by the 1930's here in the States.
Another thing working against GSK is the fact that he and his siblings were military brats. So if investigators were able to nail down the identity of the father, I'd imagine the military records angle would have been fairly easy to nail down. It must have been a PITA to get to that point, though. Pre-Social Security. People were mobile as immigrants, as well as the Great Depression saw a lot of migration.
Keeping my fingers crossed they have DNA for BG...
JMO