I agree with you on multiple accounts. Seems like the writing was lacking. In addition to not securing the hallucinating guy, they also made no formal announcement to security or to warn others about his dangerous presence. You would think with such a huge crew complement that there would be more people walking the halls in the scenes when they were trying to apprehend him. Or at least folks trying to figure out why it is dark, etc.
Also agree with the lack of direction on Carol Kane’s character. In fact, the way they included Hemmer as a hallucination, in the pre-recorded video, as well as in commentary by Una and Pelia, it almost seemed as if they were apologizing to the audience for getting rid of the Hemmer character. I am unsure of the reasoning behind it, but I thought he was a great character and wish they hadn’t killed him off.
So far this is the first episode that kind of disappointed me in the new series. It almost felt like it was filler to create the establishment of relationships between Kirk and the rest of the Enterprise crew.