In my opinion, the main downside to tying off using a running bowline to a branch is that you must reach your tie in point to remove the rope. Normally, that's not a problem. But, for instance, when you get that last minute emergency call, and you need to bail off the jobsite, you still have to go up and retrieve your rope. Terminating your rope around the trunk alleviates that concern. I could come up with a number of other reasons, but I think you get my point. I know I've had to stop what I'm doing, and change gears to another job or task, and if my rope is committed to the tree it becomes a major downside.
Also, I've read that SRT is now approved (or being approved) to work from, so you don't have to ask a groundhog to untie your anchor end.