For quite a number of years, my duty/SD/HD shotguns ran Surefire forends with the built-in lights. (I own my duty weapons.) My wife's 870 still has one on it. I later moved to a GG&G forend, which has a short piece of rail, upon which an X200 is sometimes perched. I am now transitioning to an AR15 for duty/SD/HD, and it will have at least an X200 on it, probably something more substantial later. I still consider my Surefire LX2 Lumamax to be my primary light for many things, including searching, but at the moment it is needed, nothing beats a light mounted on the long weapon. Even if found justified or otherwise legally excusable, shooting an unintended person is not something I want burdening my mind.
FWIW, I have worked for a big-city PD for 27 years now, and counting, with 26 of those years on night shift patrol. I have "cleared" MANY houses and other buildings, which could be considered successful "home invasion" scenarios. I don't work for Surefire, nor profit from their sales. I have trusted their products for years, ever since the 6P and 9P were their main notable products. (OTOH, I seem jinxed regarding Streamlight products, though I am aware that others love their products.) I don't drink all of the Surefire "kool-aid" regarding low-light fighting, but most of it is valid.
If nothing else, at times there is enough light for me to see him as a reasonable, probable threat, and him to see me, but not enough light for us to ID each other, that is when a weapon-mounted light beats a hand-held.