So, if you look at the numbers, the risk of death from climbing is very, very low. Really, it's extremely low. You'd have to go on two outings a week for 3,200 years for the probability of your death to have an expected value of 1.0. Or, if you stick to top ropes, a lot longer than that.
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.
That's still wrong. If you have x chance of surviving each day of rock climbing then you have an x^n chance of surviving n days of rock climbing, not a 0 chance of surviving.
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.