Absolutely nothing wrong with carrying TQs all over you, I do as well.
With that said, @AMC makes a good note. TQs with plastic windlasses and plastic retaining clips should NOT be carried exposed unless they're being regularly replaced. The original rec's from NAR were based off field use in Iraq and Afghanistan; granted, a cop in the US probably isn't exposing his TQ to as much UV as an infantryman doing patrols everyday in the blazing sun given a large part of the day is spent going inside buildings, in the vehicle, etc. So, in the aim of being a voice of reason instead of being a stick in the mud, Im guessing you could probably push past the NAR recommendation (90 or 120 days, cant remember which).
However, it's not a risk worth taking considering the extreme nature of when you actually need to use that TQ. If using CATs, either replace it regularly or cover that shit up so it doesn't snap on you from UV degradation.