Free: Contests & Raffles.
I agree with wreckerman they do not have enough penetrating power. When they were legal in this State I saw two bucks hit hard and did not go down 1 with a .22-250 and the other with a .233. We tracked the two bucks for 3 days and never found them on public land they both went into tribal land that we could not hunt. Unfortunately I was not in a safe position to use my .243. The only deer taken that year was with an old Winchester 38-55.
Shoot them in the head and there is plenty of penatration. Use my 22-250 to kill deer and my uncle has a .223 dpms ar15 that has killed its share of animals too. Shooting a deer in the side gets me an butt whoopin we are taught from a young age that a head shot is the only one to take. Grandpa used to chew us and tell us we wasted to much meat. We dont even use the 30-06 that every one else seems to shoot them with.
I think a major issue with allowing 22 centerfires for big game is bullet choice (as has been stated). When you get into 24 cal centerfire cartridges, most off the shelf ammo you'll find at typical sporting goods retailers is designed for big game hunting. Drop down to any 22 cal cartridge and most are either FMJ or highly frangible varmint type bullets. The informed user can choose appropriate ammunition for deer hunting in 22 caliber weapons, but many hunters do not fit this classification. Many would buy the cheapest ammo in the shelf (likely varmint type) and go hunting. This is a recipe for lots of wounded animals. That's my theory on the matter.