Right, this is also important info. They did, early this year, ask the murderer for a voluntary DNA sample, and they had received a tip that placed the murderer

Right, this is also important info. They did, early this year, ask the murderer for a voluntary DNA sample, and they had received a tip that placed the murderer on the police radar. It's possible they would have solved it eventually, but it's unlikely the police would have been allowed to forcibly collect DNA based on a vague tip that amounted to "he owned a similar hat and had discussed violence in his teens". To forcibly collect someone's DNA, the authorities need to establish the person as a reasonable suspect (skäligen misstänkt), which requires a preponderance of evidence and isn't that easy to establish. In this case, the police would have definitely needed more than the person fitting the same vague profile as thousands of others, and it was definitely hard to obtain any extra evidence given that the murderer indeed lacked any connection to the victims or to the crime scene.