Hermes, agreed, but I think we are talking about two kinds of fears. Both Seneca and modern cognitive science distinguishes the insuppressible feeling you are talking about from the slow maturing, more cognitive version of the emotion, which is the result of the feeling plus cognitive judgments (such as “I am undatable, nobody is going to like me,” etc.).
Rock climbing, I assume, puts you constantly subjected to the first kind, because you could fall at any time. But if you suffered from the second kind, you simply wouldn’t go climbing in the first place. Like I don’t.