It doesn't matter if the TOGA switch is inhibited after WOW, the GA procedure includes verify thrust which this crew simply did not do.
Consider if it had been a more normal GA as all airline pilots train for, but the TOGA switch was broken or the autothrottle failed. They would still have crashed as they were not checking the thrust. This might be an interesting scenario to throw at crews when they do the GA simulator check, fail the autothrottle just as they are about to push the TOGA button.