I remember from the report that the KLM crew said "we are now at Takeoff" and then took off with out a clearance. Not sure what difference it would have made if the had said something different like "we are now at departure".
If the word "takeoff" had never been used until a takeoff clearance is given, ATC might have picked up on the term "takeoff" as signifying the aircraft was by then in its takeoff roll.
If I call the tower and say "ready for takeoff", how is that going to lead me to misunderstand the next ATC statement to me, leading to me rolling without a clearance?
It will not, but that is not the point of that particular phraseology change.
There were two issues identified in the Tenerife accident leading to two different changes in phraseology.
1. The captain thought he had received a takeoff clearance, when he actually had only received his airways clearance. This was fixed by ensuring the takeoff and the airways clearances are given separately, so nobody could misunderstand an airways clearance as being both an airways
and a takeoff clearance.
2. When the FO told ATC "we are now at takeoff", ATC could interpret that as meaning the aircraft was ready for takeoff, or at the takeoff position, or something of that sort. That was fixed by ensuring the term "takeoff" is only used in the takeoff clearance, so whenever someone says the word "takeoff" it means someone is in the process of taking off. That makes it easier for ATC to realize when someone is taking off without a takeoff clearance.
The above illustrates that the phraseology changes introduced after Tenerife would have constituted two more barriers, that were not in place at the time of the accident, each of which would have had the possibility of preventing the accident.