Thank you for that. I've had this conversation tons of times and I've almost never had someone provide a concrete example like that. It's almost always rooted in "conventional wisdom" or "never tried it but sure it wouldn't work", or "made a perfect shot and he still runnoft".
I've read a fair bit from dog trackers that do big game recovery and they all say the same thing... For every one they recover that was shot well and ran a long way, there's 20 that were "hit great but the bullet blew up on the shoulder" that ended up having a hole in the leg or guts or brisket or anywhere but the vitals.
I do think it's heavily bullet dependant, and the smaller the bullet is the more critical it is to use a good one. There's lots of .30 cal bullets that will be anywhere from moderately effective to really effective, and some that aren't going to work well. There's lots of 6mm bullets that won't work very well, an few that work fine, and a few that are excellent.
Thankfully I haven't been part of many rodeos. I haven't been part of any that were due to too little gun. I have been on a couple that were due to poor shooting, usually connected to rifles the shooter was afraid of.
Again, I appreciate the real life experience that informs your opinion. If I had that happen to my wife or kid I might feel differently than I do.