Here's a different perspective.
I started learning traditional West African drumming (from the Ewe of Ghana). In Africa they were probably drumming with sticks before the military grip for snares was developed in European countries. So my "traditional" is different. It is what you call matched, and it needs to be because of some of the other things you do with sticks on skins (like closed or press beats which are more than just ghost notes). That's the traditional grip of traditional (pre industrial) societies.
A couple of decades later I started taking kit drum lessons and began with symmetric (what you guys call matched) grip. Then I worked on asymmetric grip, and I've continued to use both. I think using both is a good thing, and you need that flexibility of approach if you are going to play other percussion instruments.
But I do have trouble with calling the later military snare grip "traditional" because of the priority of traditional societies using a symmetric grip. But Anthropology will do that to you. DOH
I know I'm the one out of line here. Maybe even walking to the beat of a different drummer. Walking
