The video shows the plane on fire before rotation. > the crew decided to continue the flight > The plane was too heavy > couldn't fly on the remaining engines > crashed.
It's not rocket science....
It's a tragedy for the passengers and their families. It's a tragedy for the pilots...in that we will be stuck flying subsonic planes for the near future because everyone is too stupid to put decent pilots in the seats up front...
The aircraft was not on fire before V1; in fact, it was perfectly safe to fly at V1. The information available to the crew did not tell them the aircraft would be unsafe to fly; what they did know is that they were on a limiting runway and that a reject after V1 was guaranteed to result in a high speed overrun. The plane was not too heavy to fly on the remaining engines, it was just moving too slow to either climb or accelerate on the remaining engines (this was a Concorde, not a B747, they work rather differently). The fire was of such magnitude that no matter what the crew did, it would still have crashed; there was nothing the crew or anybody else could have done to control the fire. The aircraft did in fact continue to fly on the remaining engines until the fire eventually brought it down. Had they been moving faster and been able to climb the fire would still have brought it down before they could have landed (it only flew for a minute and there was nowhere to land within that time even if they had been able to climb a few hundred feet higher).
Had they rejected they would have gone off the end doing some 100 kts, with a plane that was already on fire, with nothing but grass to brake on and with the cargo village at the other end. It is extremely unlikely that anyone onboard would have survived the reject.
This was not a human error or human factors accident, but one of those rare purely technical events. The crash happened because a mechanism existed by which a tyre failure after V1 could render the plane unable to fly at a stage where it was too late to safely reject, leaving no sure options to avoid a disaster, and because FOD triggered that mechanism.