While it is true that that an object will give way at the moment of greatest force (the initial impact), the object falling will loose some of its speed.
This is because a certain energy is required to collapse the standing object (your head). This energy comes from the falling object and is transitioned on impact. Therefore the falling object looses energy, in the case in the form of speed. So it would slow down and have to accelerate again.
In the case of the anvil and your head, the energy transferred would be small due to the large mass of the anvil (resulting in a high momentum) and small mass and weak structural support of your body. Therefore the anvil would still be traveling pretty fast, and continuously collide into your body until either you reach the same speed as the anvil or you both are stopped by the larger structural support of the ground.
In the case of the towers where you have the opposite. There is a relatively small mass falling compared to the large mass and high structural support below it. In this case you would expect nearly all of the falling floors energy to be transferred to the structure to collapse it. Some may argue that it would require more energy than the first floors that fell had. Ignoring that possibility you still have to accept that the falling floors (the initial and the newly collapsed) have lost all their momentum due to the impact and have to accelerate again.
Because of this the tower would never fall at free fall speeds. It would be must slower due to the resistance below it. And this is the critical detail that can never be hidden but is ignored. No matter what you debunk, unless you disprove gravity you cannot refute it.
Now I will say that as the floors collapse, more mass is falling in proportion to the structure below it. Therefore it would accelerate as it reached the bottom. But this does not change the original conclusion.
There was a video recently about a 9/11 theory (free energy or something but it had several good points/questions brought up). In this video they examined what would happen if only 1/10th the floors were there, allowing the building to free fall through 9/10 of them. Even this assumption gave a fall time several times the actual fall time.