Good point big picture, but in my mind after TOGA button and a fist full of thrust in a light 73 there is little hope of being able to engage automation. Control yoke pressure has to be completely released which isn't going to happen when you are struggling to keep the nose from rearing up. Same as on the classic.
Initially, I agree with you, as it’s likely out-of-trim and somewhat of a handful. However, in the time it takes to get to 3,000’, one would have hoped for an opportunity to sort things out in terms of pitch trim and automation. Even if you just let go and engaged the autopilot, it would sort itself out to some degree - maybe not pretty but at least the stabiliser would be returned to a normal position for the stage of flight rather than trimmed into oblivion.
There was an excess of speed and thrust, so why was the response to pitch/trim down and reapply full thrust? This could likely give the answer but we may never know...