First off, unless my aircraft reognition is way off. That was a C182, a bit more power than a 172.
I saw that video before and to me it looks more like a typical density altitude type accident. It never seems to leave ground effect, or at least does so at a very low airspeed and high AOA. Even if a light aircraft is not overloaded for normal conditions and the C of G is within limits, under certain conditons an aircraft will fly forever, 20 feet off the ground on the verge of stalling.
As it was Columbia, we can assume it was hot. The wind looked calm or light. We can see it was a rough dirt strip, possibly at altitude. I imagine the density altitude was several thousand feet above the actual altitude. Many people don't realise how much an aircraft's performance falls off at altitude and how much runway even a light aircraft needs to get airborne on hot days. Combine the two and the result it what we see in the video.
According to my 172 manual, (the only one I have), take off distance to 50 feet at sea level with max weight and 10deg C is 918 feet. At 7000 feet and 30 degC it's 2221. An extra 1303 feet. That's on a paved runway with a new aircraft. That difference is enough to kill you.
I could be wrong and maybe somewhere there is an official analysis of the accident. But it's at least a contributory factor.
