I have been using the method I mentioned for years. I hunt public land with a climbing stand, I never know if I will have to move my stand. ( someone beats me to the spot, or the weather...) so the attached safety climbing rope from the top of the tree will not work for me. I would have to climb the tree and undo it and then climb back down the tree.
I agree if you have a set location or lock on tree stands , that method would work best.
For that matter even a ladder stand, any time you are off the ground you should have a safety vest on.

Another very important part to this is, TAKE Your TIME! Guys get in a hurry and are rushing or decide to climb up or down without being attached to the tree, this is when most accidents happen.

This video shows the technique I use to climb the tree.
https://youtu.be/6ps8Q2EyWQk