Did you read my post? I did this from 8 inch to 18 inch drums. I have some video/pics if you need to see this. I'm fairly familiar with the physics of the membranous sound cylinder we're working with here. All I said was, in my experience, there was a difference. I leave it up to you to experiment with a simple 14 inch batter hoop. You make your own call. If you hear a difference, then there is. If you don't, then there's not. No argument and no point to refute. It's always up to the drummers own ears to make the call.
Here's one of the kits I worked the wood hoops on. I also did this with my Recording Custom kit and one other. If you look closely, the snare is the Recording Custom snare. The other snare to my left is a Trick with diecast hoops. I've also included a pic of the same Recording Custom snare with the wood hoops.