There is good reason many states do not allow .22 cal for deer
For every sportsman out there willing to take the time to take only a good shot, spend the money to use a bullet built for the game, and do their best to kill cleanly, there are the "slob hunters" who will take any shot offered, use the cheapest ammo, and seldom adhere to the general rules of sport hunting.
For decades, .22 cal rifles (centerfire) were only varmint rounds, and bullets suitable for deer were few and far between. Many states decided that while it could be done well, it was seldom done well with a .22 CF, and people being what they are, if allowed there would be a lot more crippled and wounded deer dying without actually being harvested. So they chose to mandate a larger caliber round for sporting use. Most states have a minimum of .24 caliber for deer.
Game laws have nothing to do with what will actually work to kill the animals, they have everything to do with what is considered "sporting".
I have not personally taken deer with a .22 centerfire, as I have not hunted anywhere it was legal to do so. There is no doubt in my mind that any .22 with the rigfht bullet for the game, and within its effective range will cleanly kill a deer with correct shot placement. If I had to hunt deer with a .22 Hornet, I would, and have no worries about it failing, so long as I did my part. I wouldn't be taking no 300 yds shots with it though!