I can recall no less than 3 little texas deer that took a .223 in the shoulder and it took 3-4 more hours of tracking for them to be recovered-last one was shot at dark, and we tracked him 3-400 yards in the dark-got close enough to hear him breathing but he was in stuff too thick for the flashlight to penetrate so we hunkered down for 1.5 hours before he gave up the ghost. Was lucky that time as the 8yo boy I was guiding that evening didn't get spooked or scared one bit in that thick creek bottom in the dark. That's been my experience with the .223 tsx. As I said, I have also seen my share go down fast with the .223 as well.
I have not had this issue with a well placed .243 bullet.
Now, if I was getting a gun specifically for the kiddos to shoot, 22lr/.223 would be just right for learning to shoot/having fun with. On deer size game I'd prefer a .243 the gun carried to the stand. And I bet when they are in the stand and squeeze one off at a live target they will not mention the felt recoil/muzzle blast.
Having said that, if All the kid has/brings is a .223 I certainly would not refuse them. I'd just stress hard proper shot placement, be prepared to make a f/u shot and bring extra flashlights in case there is a need for extended tracking.
