Having a light on the weapon has never made any sense to me.
In the second or so that you are moving the light back and forth to find the bad guy, the bad guy has a lighted target to shoot at that you are holding right in front of your face.
Why is that a ever good idea?
Years ago in Law Enforcement training we were tought to think just like you but it never made sence to me. We are told to hold our light way out to our side to throw off the bad guy which actualy can throw you off ballance and is no good at all in door ways as it would let the bad guy know you are headed his way before you got there. Hell they even said that before entering a room we should lay our flash light on the floor just inside the door way and roll it into the room in a way that it would roll and light up the entire room. Ok now my light is in the room and I am outside of the room in the dark with no light and have to enter the room to get my light

What if the BG is in there behind or under something and I did not see him as my light rolled across the floor

Now I am going to enter the room thinking it is clear and get my ass shot off trying to get my light back. Thank God we are not tought this technique anymore.
Not to mention that having the light mounted to the weapon alows you to use both hands to control your weapon just like most people train. We have to shoot with our strong hand only and weak hand only when we qualify with our backup and off duty weapons so I can tell you for a fact that 2 hands is better than one when it comes to controling a firearm. We also have to do a night fire qualification every year and those that use the weapon mounted lights and shoot with both hands on the gun do far better than those that have to hold a light in one hand and shoot with the other.
Sorry for the inverted pic, I havent figured out how to stop my Iphone from doing this.
Light on bedroom door at ruffly 15 feet, both hands on gun for better control if someone (bad guy) was to come in.