If your assured of hanging from small enough trees then a shorter tree strap is really all that is needed. I don't see the point in attaching rope to both ends of the strap to attach to your hammock suspension line. If the rope is coming into contact with the tree then your tree straps are to short and you run the risk of damaging the tree. That is what most of us are doing with the tree strap in the first place, protecting the tree and protecting our ability to hang from them. People start leaving marks on trees because they aren't using long enough tree straps and our ability to hang from the trees will be rapidly outlawed.
You can argue whether it actually hurts the tree or not but if it leaves marks it will be bad for hangers.