The crash was essentially due to additional factors, one being that they descended to 30ft over a runway that they could not land on when they were supposed to fly past at a minimum of 100ft if this was the case. This affected the flight control systems, disabling some of the protections that are inhibited if you are intending to land.
When they realised that they were too low and selected takeoff/go-around thrust, the spool up time of the engines was about 7 seconds, by the time the engines had increased thrust from near idle power they were busily ingesting tree branches and naturally flamed out as the combustion chambers filled up with crushed wood.
The A320 was very new then, and a lot more is known about the Airbus flight control systems now. The aircraft did what it was told to do, the flight crew were just a little bit ignorant about the corner case they were exploring.