Explain why tree houses don’t change in height as a tree grows?

The reason tree houses are observed not to change in height lies in the way a tree grows. New growth occurs at buds, essentially adding on to the tips of branches. Existing branches, limbs, and trunk grow wider, but not longer. The wood in the center of the trunk and branches ceases to be actively involved in transporting water and nutrients up and down; fresh new tissue is added at the outside every year to fulfill that function. This newly added living tissue causes the trunk and branches to widen year by year. They do not lengthen, however. The older wood at their centers is often described as “dead,” and is not growing at all. It provides structural support to the tree, of course, but it basically sits there, unchanged.
It is easy for a tree to add new tissue at the buds at the tips of branches and in a layer around the trunk and all branches. In the other hand, it would be a complicated feat of engineering to lengthen the “dead” wood at the center of the trunk, hoisting all the mass of trunk and branches higher in the air. Thus established branches stay where they are, just lengthening and widening, and adornments such as tree houses and carved initials also remain in place.