Aside from being able to control your handgun with a normal grip, the obvious benefit of a weapon-mounted light is that it takes no more coordinated effort or skill to use it with a firearm. Where you point your gun is where your light shines. You can assess any threat without the constant need to work at keeping the gun and light focused on the same point.
They are small enough now that many people keep a light mounted to the gun all the time, so it’s there when you need it. Holster makers are responding by offering new rigs designed to fit handguns with lights and lasers attached. DeSantis Gunhide, for instance, has its leather Tac-Lite (with thumb break) and Speed-Lite (without thumb break) holsters for use with TLR-8equipped guns.
If you don’t want the light attached full time, they’re easy to remove. You can carry the gun all day, then add the light when you reach your destination, whether that’s a remote wooded area, a hotel in a strange town or home sweet home. They make great handheld lights off of the gun too. That’s a good idea because often you don’t want to be pointing a gun where you need to direct your light.