Why don't mall cops need to carry guns?

"Mall cops" usually aren't actual police officers - they're typically security guards limited to their duties to observe and report. This is so for a number of reasons. There will usually be a police presence at a mall, unarmed security guards require less training and quaification (in turn, allowing them to be paid less), and mall owners typically don't want the liability associated with having armed security present - a missed shot which hits a bystander would almost certainly result in a devastating lawsuit against the company which hired the armed security service.