Wow, this is a weird one to get into, but what the hey! That's never shut me up before.
As far as destroying tissue and bleeding out an animal, well isn't that what an arrow or spear does? An arrow can cause an immense amount of internal bleeding, and cause a pretty quick death, but I've seen too many deer shot with arrows to do it myself.
I hunt with a wildcat cartridge that is the ballistic equivalent of a 30-06. It kills game really well, so far at least. Over the years I have shot several deer with a 22-250 and never had one go further than maybe 25 yards after being hit in the boiler works. I've shot several more with a 6mm Rem with more or less the same results. Same with a 30-30. A friend of mine regularly shoots deer out of his back door (in daylight) with a .22 mag and has never had one get away.
I find it interesting that people hesitate to state that a .243 is an adequate deer round because they don't know who might read that in cyber-space and then go wound some poor deer due to bad shooting with a small caliber round.
In my great-grandfathers time and before, many, many, many deer and bear were shot and killed with Kentucky long rifles in calibers as small as .32 or .36 that had about the same muzzle energy as a .25-20. The trick was the hunters knew how to hunt, hunted for their food and, more than likely, didn't take too many less than optimum shots. Especially with bears.
There's the rub - it's not about the gun, it's about the gunner. Thinking that a bigger gun will make up for a poor shot is simply foolishness.
If someone wants to hunt deer with a modern repo .45 cal muzzle loader no one bats an eye. They are expected to shoot within a reasonable range for their weapon. Same with a bow, isn't it?
If some idiot goes out with a gun he or she can't handle well or shoots at ranges that are beyond their skill level, well, the problem lies not with the gun.
Too many inexperienced people are hitting the woods without the skills necessary to be a skilled hunter. Things are different now than they were when I first started hunting in the '60s. Back then a new hunter was usually a kid who was mentored by an older relative or family friend. He (for he was usually a boy) was first trained in firearm safety and woe be it to the kid that screwed up with a gun, even once. Only after showing reasonable competence with a firearm was the tyro allowed to go along on the hunt. Not so nowadays. People can take the 'Hunter Safety' test on-line with the answers readily available. Too many yahoos in the field these days. If you don't believe me just watch the news during hunting season.
If my life or my family's life depended on my killing a deer with a .22rf I have no doubt I could do it. I'd rather have something bigger, but it wouldn't be about the gun, it would be about the hunter.
Have respect for the game you hunt. Like Rourke said, use enough gun. What comprises enough gun is up to you. You must know how to shoot, but more importantly you must know how to hunt.