The centerfire .22s are very popular in the Hill Country of Texas, so I've heard these tales of woe from several people, including close relatives, one a cousin that was in my wedding. I've also heard similar tales from bowhunter's. I've looked for a head-shot hog in a pine thicket - all we found was was the base of the bullet from the .44 mag used on it. I've tracked and killed deer wounded, but still able to trot, that was shot with .270.

So I have heard the tales, but they just aren't repeated to a wide audience.

No, I've never shot a deer with .22 centerfire and I never intend to try. They are used a lot to kill deer. However, I can say this, a big deer shot on the shoulder (not behind the shoulder) with run of the mill factory ammo runs a very high risk of being wounded and lost. A big game bullet from something as small as .243 Win probably ends up on the other side of the animal if not exiting. And how big of a wound does it take to kill or cripple a deer? Not much. A blown out hole as big as a golf ball is enough to set in infection or shatter a shoulder bone such that the deer, if it survives, is a cripple from then on out.

BTW, I've killed two fist fulls of deer with a 6mm Rem, never had on get away that was hit. But, I eventually went to Nosler Partitions, then upgraded to a .308, then a .300 Win Mag (when my wife took over the .308), and have just recently rebarrelled the 6mm to .260. Why? Because when confronted with a good hog or big buck I wanted a little more insurance than the 6mm just in case something less than a perfect, broadside shot was presented. When you've spent as much money and time in the woods as I have, you don't want to pass up that "buck of a lifetime" because he is quartering away and only gives you 2 seconds to pull the trigger as he moving through the oaks trailing a doe. I killed my biggest deer ever with the .300 Win Mag when he paused too long in the shooting lane. He started to move when I pulled the trigger and I hit him in the back of the lungs. I found him about 30 ft from the spot of the shot. I don't think it would have been that soon with a similar shot from the 6mm.

I love to tell this tale: When I lived in Tenn, each fall a LOL (little old lady) friend of mine would take her cane in one hand and her .22 single shot rifle (open sights) in the other and stump down to the orchard. There she would shoot a nice spike or 2x2 buck deer. She would come back to the house and drive her riding mower to the orchard and drag the deer home. Imagine if you will, a chubby LOL, in a house dress, apron, bifocals perched on the end of her nose and a hair net, skinning and cutting up a deer. Kinda cute.
Does this mean a .22LR is a deer round? Poachers use them quite a bit. IMO, not hardly. No matter how many "I use factory ammo and they drop like a sack of oats" stories I hear. Like the targets with the lousy groups that get torn up and left at the range, you don't hear about the deer shot in the ass, or hams, or shoulder that run away. "Hell, he didn't act like he was hit; ain't no reason to go and check."