When the tree survives and grows in a different manner, how is anyone able to explain the "it harms the tree" principle? The cuts scar over and the energy in the tree is expended in some other area. The pines that I have topped for years now have all done just fine and actually thicken, creating as canopy above the woods floor. Nobody in their right mind just goes in and cuts a tree in half like the picture above. Like a haircut, you need to blend the remaining branches with what is left. I have done this to oaks, pines, maples and even leland cypruss, cutting the lead and pruning around the remaining top edges to blend it better. Some trees do not take well to cutting and pruning and others continue to grow. I always explain this to the HO before cutting and tell them no guarantees.
It's all about what happens to the tree internally that makes a differfence. When you top a tree, you force it to deplete its energy reserves in order to replenish the growth that it has lost. A topped tree begins to starve because it now has only a fraciton of the leaves it had previous to being topped. As a result, it cannot take in enough sunlight to produce photosynthesis which is how a tree gets its energy along with getting nutrients from the soil.
Most topped trees do put on a sudden flush of new growth after being topped and, on the outside, they can appear look healthy and vigorous. But, on the inside, the tree is getting weaker and weaker as its energy reserves get lower and lower. Over a period of years, the tree puts on new growth as fast as it can (often in the form of watersprouts) to keep from 'starving' to death.
In a healthy tree, energy created through photosynthesis is typically allocated towards two things - putting on new growth and building up defense (think of it like an imune system). If a topped tree is forced to put all of its energy towards replenishing a topped canopy, then it suddenly is left short of enough energy to put towards defense.
As a result, it may take 5, 10, even more years but, eventually some pest or disease comes along and attacks the tree and it doesn't have enough energy built up in its reserves to defend against it and it goes downhill quickly from there and ends up firewood whereas a healthy tree with sufficient energy in its defense reserves would have a much better chance at defending itself.
Think of it this way...a person with HIV or AIDS doesn't typically die from HIV or AIDS. Rather, it's pneumonia or something else that attacks the person's depleted immune system and gets the best of them whereas a person with a healthy immune system is able to fight off the attack.
If you continually stress out a tree, whether it be by topping, root cutting, improper fertilization or some other inappropriate treatment, the tree may look fine on the outside but there is a whole lot of bad stuff going on on the inside.