Limiting innings is NOT the answer, though I don't know what the answer is and doubt there even is an answer. The kids who want to be good will work very hard at it. There is no such thing as a stud pitcher that just fell out of bed able to pitch at a high level, they have to throw a lot! Same thing with a hitter. The swings they make in a game are just a fraction of what they do in practice. To me, it's the practice that produces the majority of the wear and tear. Some can take it and be very good at the sport. Some can't and never reach their potential.
A while back someone posted something about how many hours of work it takes to be world class elite at something. It's a lot of time (was it something like 10,000 hours?) and it will take it's toll. I suspect that very few if any serious athletes get through their career without having some sort of lingering issue with their bodies as they age. That said, how many regret the work (and damage) they did to get there? You can say the kid can't make the decision themselves, but if you as a parent don't allow it until the kid can decide for themselves, then it's too late to even try.
Any sort of sports career is a risk. The better the player wants to be, the higher the risk of injury. Is it child abuse to let a kid out in the sun? Take a kid someplace in a car? Climbing trees? Playing tag? Take a bath? Kids can and do get hurt and even killed doing these things all the time. Life is a risk, or you can just go hide in a bunker.
I suppose MY answer would be the smart coach and the smart player have to know when enough is enough. There is no one size fits all answer to that question, nor should there be.
PS This is coming from a pitcher's dad who was a number 3, a 2, and a 1 at various times. A kid who also has had stress fractures in her back and plenty of sore arms over the years. And who also holds a bunch of school records in college. Yes, there was a price to pay and I am sure she thinks "Was it worth it?" is a ridiculous question!