>Heck, there used to be a myth that in an impending head-on collision you would speed up because that would put most of the force onto the other car and reduce your own damage. (That's not really how that works, of course)

That's the advice for when you're gonna hit a large animal. Getting off the brake raises the nose lessening the chance the animal will wind up sharing the passenger cabin with you. It's not totally invalid but pretty dated. With the low hoods of modern cars Bambi is gonna wind up in the passenger seat damn near every time. If you're driving some 50s-70s brick then it holds more water.