A person who is afraid of failure might spend the most productive and energetic years of his life trying to prove that he is worth something, becoming successful as a side effect.
That's the point though. In some cases we allow fears to get in our way and stop us doing things. If someone uses those fears in a positive way and actually does something then it is not really a problem.
That's true. But it can be a problem if you dedicate your life into something not because you are really enjoying it but because you want to prove to yourself (and others) that you are successful, strong, etc. There are many people I can think of who do things in order to impress and be accepted by others, not because they are really enjoying them. In this case they are not paralyzed by fear but they are using it as a wrong motivation.
Very true.