Most of the original bags extant are from the 19th century, so it's hard to say how common button closures would have been in earlier times. I would suggest they would have been on bags where the user expected or found from experience that hard usage, personal slips/falls, and crossing large streams or rivers would have required a bag closure of some sort. Yes, the rifle and bag and horn would have been carried above the person's head when crossing streams and rivers, but that doesn't mean one wouldn't slip or fall IN the water and spill contents from the bag with no closure on it.
The guys who only used their bags for hunting and where no hostiles were around, may have found no need for a closure, especially with the long flaps Jeff mentioned. Then again, in hostile country, one may have wanted no closure or at least unbuttoned the pouch flap if he sensed or expected hostiles. Personally I prefer a closure of some type and then have the option of leaving it unbuttoned when I prefer to do so.
I think we have to be a bit careful when drawing too many conclusions from original bags, as well because leather is a perishable item. I would suggest the bags that are extant are due in at least some major part to the fact they weren't used as much as other bags. A bag that is only taken off the wall for hunting would most likely survive longer than a bag that was actually worn on the person every day in the harsh elements and over various terrain.
Bottom line, if one wishes to use a period button or other type of period closure, there should be no reason not to do so. Or, if the person wishes not to have one, that is their choice just as it was over 200 or more years ago.
Gus