When you are a head detective you are almost always in constant danger. Sure, carrying a gun is reassuring, but it's not always helpful or usable.
And, if you are a meddling, childish, fake psychic, you are also in constant danger. Plus, then you don't get the advantage of a gun.
Still, the two men participated in these lethal habits on a daily basis. When one of them has a near death encounter the other is always there to hold them and kiss them and tell them everything is ok.
And sometimes that is way better than having a gun.