Your argument doesn't dispute the fact that in an emergency stop, which is the ultimate nightmare scenario in slick road conditions, power distribution to all wheels just doesn't make enough difference to justify driving any differently than if you were in a FWD vehicle. The video you linked is two vehicles in a fairly low-speed controlled situation.

4wd/AWD helps you move forward in adverse conditions. In an emergency stop situation it makes no difference. Having a better grip on the road surface is great, but an all-wheel vehicle should be operated no differently than a 2wd vehicle if conditions are poor.