Power is largely irrelavent when pulling out at the bottom of the manouver. Whilst the nose is pointed downwards, power just increases your speed towards the ground - and gravity is already pulling you down. What you need is lift - which can only come from getting the wings level.
i'm surprised at that for a fighter aircraft, even for an old one. i would have thought if you put on full power and pull back on the stick it would pretty sharply turn up, not increase your speed towards the ground.
even if the stick is pulled back too much i'd expect it to be more difficult to stall the jet than it appeared, providing power was on full. at the end it looks like he pulled back without power and it fell like a stone. didn't hear any engine noise increase.
Lift can only come from two sources - the wings providing aerodynamic lift, and/or the engine thrust being pointed downwards.
The axis of engine thrust is basically in line with the fuselage. If the nose is pointed down, then simple physics says a proportion of that thrust is accelerating the plane towards the ground. This doesn't stop until the fuselage is level, at which point all the thrust is accelerating the aircraft forwards. If you're coming down off a loop, then gravity is already accelerating you towards the ground, so you don't really want the engine thrusting you even faster downwards. AIUI, the normal technique is full power from 6 to 10 o-clock (to gain height), then ease off the throttle between 11 and 12 o-clock on the way up, and then feed the throttle back in again at about 5 o-clock on the way down (once you know you're pulling out successfully).
The Hunter isn't a particularly powerful aeroplane - not when compared to a modern jet like an F-16, Typhoon or Tornado or F-4. Pulling hard on the stick will create a lot of drag, which will cause a loss of speed/energy. If the engine isn't producing enough thrust to overcome the loss of energy then the plane will eventually stall. There is an optimum speed and power setting to achieve a min radius turn/loop - but the critical point is not at the bottom - it's at the top. If you don't hit your gate speed/altitude then it doesn't matter what you do on the way down you are going to bust the minimums.
There was a fatal F-4 phantom crash on the practice day for RAF Abingdon back in the late 80's. The main factor was found to be that the pilot had spent too long with the throttles full open at the top of the loop. This meant that his speed through the "gate" was too high, and therefore the radius of the turn in the second half of the loop was wider than he expected, and ultimately greater than the altitude available to recover.
Everyone needs to wait for the full AAIB report before coming to any conclusions here.