Nothing wrong with shooting smaller calibers but you have absolutely got to be picky with shot placement. I have hunted deer with a 22-250 for 18ish years now. I only shoot them in the neck or head and I have only lost one deer doing so. Sure, I have to pass on a fair number of deer because I can't get a clean shot but when I do pull the trigger, I do not mess up any meat, I do not have to track a deer, and the animal doesn't have to suffer. In the end, it's worth it to me.
What about the one you mentioned you loss, probably shot off its bottom jaw....he/she suffer????