Compared to how much you can benefit from the exercise, the risk of falling and dying is really insignificant, to the point that I don't think it's worth debating between climbing and any other common form of exercise.
[EDIT]: Fix an incorrectly worded statement about expected value.
My uncle played football in high-school, broke his knee and it's bothered him ever since. He didn't die.
Everything we do has risk, and we shouldn't let it consume us. But I'd also not focus on death in isolation.
> the benefits of exercise massively outweigh the risks of even a dangerous activity like climbing.
In other words, the risks of heart attack, diabetes and other diseases are worse than rock climbing, even if you go climbing twice a week.