Health benefits would not come from the trad bow side, but from multiple things that are involved. You can gun hunt, fish, or go for a hike and have the same results to help with health benefits.
The biggest benefit that comes to mind is getting rid of stress. Work, Kids, illness, cleaning, and other things can build up which can be huge. Those were mine this week and that is nothing compared to some others people have. When I was LEO stress was insane, but for me when I am out in the woods or on a lake, maybe even fishing that stuff seems to disappear for awhile and when you get home your able to deal with the problems at hand better which leads to less stress.
Remember when you are hunting that every single second should be stress free and in order to do that you need to be safe as possible.