Are there any benefits to flavor by chewing with your mouth open?
I don’t think so, unless you are experiencing so with other foods. Why would there be?
ISTM chewing with mouth open, or more to the point, breathing through mouth with food in mouth, enhances flavor. My guess: This brings the olfactory sense more into play.
And a possible drawback to doing so would be to breathe in too hard and end up choking.