We used to hang from a waist belt strap ( me) and a full body harness ( my partner) at every bowhunter and hunter ed class we taught for several years until we had videos made.
I for one don't see a lot of reason to change to a rock climber belt. I don't use a climber, preferring steps up the tree, and with those in place we were NEVER unable to just get ourselves back up or back onto the steps. A climber might be a bit trickier.
BTW, using the belt strap, over half the time I was suspended nearly upside down and could not "save" myself, needing help from the crew. Not to mention the large probability of broken ribs if you actually "fall" or the stand collapses vs just leaning off the stand and swinging as we did.
I understand there is the potential for trauma in time, but we never saw the situation where we couldn't just turn around and re-climb.
ChuckC