If girdling is so much better biologically, why is cut-pile-burn the most widely used practice? These are my opinions. First, there is the aesthetic of making the work obvious (our pile shows how hard we worked) and neat (we did not leave a mess). Second, girdling result in a slow death and provides time for many individuals observe that someone is trying to kill a tree. It stresses many people to be reminded of death. Third, people like to work in groups and stay together. With cut-pile-burn the group does not cover much ground and they come back to that place for subsequent stages of the activity (rarely is the pile burnt on the day it is constructed.) Fourth, after death the woody stem remains standing for some time. If the girdled stem is a tree, one has the potential for damage to someone or something when it eventually does fall and associated legal liability. If the girdled stems are small trees, there is an aesthetic problem of dead twigs that persists for a few years.
In conclusion, cut-pile-burn offends fewer people and it pleases workers, so it continues to be the preferred technique even though it is not efficient (measured in restored area per person hour effort).