That is part of the point of using smaller chamberings for big game. With today's bullet designs they are much more effective than yesteryears bullets.
The two main reasons given for lack of practice is money and recoil. The .223 solves both. An average hunter can effectively hit within 2-4 inches of where they aim 90% of the time, given a bit of practice. You don't have to be an exceptional shooter. Everyone I have put behind a small caliber rifle is much more effective on target than they are with their bigger guns. Contrary to popular belief deer and elk are not armor-plated. Their vital zone is quite large as well. Put a bullet in there and they die. Period.
As for the "conventional wisdom" regarding a bigger bullet bieng able to compensate for poor shot placement, that is just BS. A small caliber, frangible bullet is actually more effective if you gut shoot them than a large caliber bonded or monometal bullet. And there is plenty of evidence that they will also penetrate bone, so that argument is also invalid. As I said to open, bullets have come a long way.