I've shot competition .22 for years. Most of that at distances twice what you mentioned here. 50-yards was where we'd start, shoot a few warm-up shots and then move out, engaging targets at 10-yard intervals starting at the 50-yard line and going all the way to 100-yards. Being able to put about 10-rounds in a group approximately the size of a ping-pong ball while kneeling, sitting, prone and if we're lucky, offhand. It's not easy. I'm not trying to be argumentative but rather trying to show that it's easy to make a shot with something smaller if you practice. Although you mentioned taking shots through brush, which is sometimes required during hunting. If a shot like that were to be taken with a .22 the bullet likely wouldn't hit the target due to deflection.
I guess I just don't see the need for all the large calibers when it can be done with less. Hell, people spear pigs and from what I've been told, will take them with nothing but a knife (now this I've got to see... while sitting out of reach of the pig) and they do it successfully. Why do we need something big to do it? The head of a pig isn't that small, I guess I just don't understand why something smaller can be used.
Is this anything like my enjoyment of shooting gophers with a .223? Actually probably not. I do that at distances farther than my Anschutz will shoot.