LE did test the knife sheath right away for DNA. They submitted it to CODIS where the murderer wasn't in the system. Thus began the journey to GGI, which is what eventually identified a potential suspect. They were also searching for the white Elantra they spotted in the area at the time of the murders.
It took hundreds of man hours to comb through CCTV footage and to obtain warrants for cellular and GPS data, SM accounts, Amazon, etc.
I think all LE involved did one he ll of a job considering the carnage and chaos they encountered and what little evidence he left at the scene. He was arrested in approximately 6 weeks. I don't believe LE would have gambled on a cooling off period, the murderer was an enigma and an unknown to them. Who's to say he wasn't going to go on another rampage?
Much respect to all of LE involved (MPD, CSI, IPD, FBI) who worked tirelessly and had this murdering psycho locked up quickly. They prevented him from killing EVER again. Had he not been arrested, I definitely believe he would have done it again and again until he was caught. He enjoyed it a lot.
JMO