I guess they (the LEO's) didn't wait because this was an "armed criminal" call so they didn't know if he was still a threat, going to become a threat again, etc.. And I'm sure that they didn't know that he had company at the time (assuming that the LEO's couldn't see inside the place due to closed blinds, second floor, etc.).
You might be sure, but you'd be wrong. According to the story, they were told that he was in the company of another person (the apartment's owner), and given the lack of indication he had a partner, they had to operate under the assumption that the other person wasn't involved.