Don't even feel my .300 Win mag when I'm shooting at a deer. Just like you say. No flinches or anything. Just aim and squeeze.
Nice thing about a magnum, no one else puts a tag on your deer. In 15 years I've shot numerous whitetail bucks (and does), a mule deer buck, two elk and a black bear and not one has gone over 10 yards from where I hit them.
Kind of mess to field dress sometimes though....