I know, and I hope that you know, that if you walk into Wal-Mart, and ask for a box of .22 bullets, the sales clerk will reach for a box of bullets with a lable that says .22 He or she may ask if you want .22 Long Rifle, but probably not, because almost all .22 ammo sold these days is Long Rifle.
Now, if you purchase that box of .22 ammo, carry it home, and load your AR with it, you'll probably not be able to fire the damned thing at all. The .22 cartridges are going to rattle around in the magazine, and never make it into the chamber. Even if you stuff a .22LR into the chamber, close the breech, and pull the trigger, it probably isn't going to fire - it's a rimfire, vs the center fire firing pin.
Let us dismiss the common .22LR for now.
I know, and I certainly hope that you know, that chambering the wrong center fire round into your center fire rifle is quite likely to result in your serious injury or death. You can play cute with terminology here, but not all ".22 caliber rifles" are the same. As you point out, the chamber isn't .22 caliber at all - the damned chamber MIGHT BE as much as an inch in diameter. The chamber tells you what size the cartridge needs to be to fit the chamber.
So far, you've not made any points that aren't obvious to anyone who knows his weapons.
Perhaps in your state, the law says that you must use bullets that are .30 or greater - I don't know what your law actually says. But I find that hard to believe. I've taken big game with .243 and .270. My dad has taken big game with a .22 Hornet - that was the only rifle he could afford to buy all those years ago before WW2. That Hornet is a sweet little gun - but it wouldn't be legal to use for big game today in either my home state, or my adopted state. It is, indeed, a .22 The .222 and the .223 are legal. The weight of the bullet, the powder charge, and even the diameter of the bullet sets them all apart from the .22.
Just give it up - you mis-spoke, and now you're trying to justify what you said. You simply cannot push all those rounds you've mentioned through the barrel of a .22 rifle. Each of them will damage the barrel, if not the chamber. Eventually, the damned rifle might even blow apart in your hands.
There's a reason why shooters are taught to always check their weapon and their ammunition to see that they match.