This is a really good question. I don't have a data-backed answer for you but I'll relay my experience.
I think climbers get injured at a slightly higher rate relative to other mainstream outdoor sports like running, backpacking, cycling (?).
I see people get hurt when the complexity of a particular objective outweighs the experience of the climber. I believe, as climbing becomes more mainstream, this will be the prevailing cause of injuries and fatalities.
However, I have also seen a terrifying phenomenon trending over my 18 years of climbing. I see more reports of highly experienced climbers getting hurt on relatively simple climbing objectives. I read a report of a guy who fell 200' to his death while attempting to rappel. Apparently, he just forgot to feed the rope through his grigri--a task he undoubtedly performed hundreds of times before.
I think we need to be more aware of those everyday risks. To take them without thinking is perfectly human. It's also perfectly human to hit a cyclist while texting during your daily commute.
Maybe that's what happened to Klein and Wells.