Ive used a .220 Swift and 55gr Trophy Bonded on Axis deer and BlackBuck Antelope, plus one 150# young mule deer buck in Utah. I've also shot a 80# shoat with a little .221 Fireball and the older 50gr XLC barnes bullet. Range was under 75yds, took out a shoulder, both lungs, ahd a 50 caliber exit hole.
My cousin uses a 22-250 on Texas whitetail, and she always kills. Its like said here, the "best' place to use a hot .22 is over bait, close range. I was limited to the above 220 Swift because I was recovering from a neck fusion and I was going stir crazy, needed to hunt! ha.
Sure, I think a 6mm is more efficient, but lots of folks use the .223, but the ones who do are not making very long shots with them. You can "hit" the deer, but good luck finding any kind of blood trail, very iffy. As I get older, I like a .270 as an all around deer rifle, and to me, the grand old 30.06 was like a "magnum" on Texas deer, ha.