Its not as simple as "Well they should've just pushed the thrust levers up at the start!" By the time they worked through their own confusion as to what was going on, time and gravity had taken overt
I think the real question 'why didn't they just push the thrust levers up at the start?'
I think the answer is not so much to do with the individual pilots involved in this incident, but more to do with how all of our brains learn and behave. For the two brains there on the day, the auto thrust had been doing it's job so reliably and so consistently in all phases of flight for so long that the sub conscious motor skill of manipulating the levers to get what is desired had eroded, conscious thought and processing was required.
This requirement for processing came at a moment in time where several other things were competing for processing bandwidth; processing the "long landing long landing" audio, processing the ATC instruction to climb straight ahead to 4000ft, processing the calls from the PM , processing what step comes next regarding flap and gear etc etc. There is a limit to how much an individual can process in a finite period of time.
The pitch and thrust should not require significant conscious thought for a professional Airline pilot. We have automated the thrust to the point where it now requires conscious effort to manipulate it because there is so rarely a requirement to do it. That is the heart of the problem IMO.