There are two problems with this strategy:
A. By the time the fear subsides, it will be too late. By the time you're not afraid of what you were planning to start/say/do, someone else will have already done it, it will already be said or it will be irrelevant. The reason you're afraid is that there's leverage here, something might happen. Which is exactly the signal you're looking for.
B. The fear certainly helps you do it better. The fear-less one might sleep better, but sleeping well doesn't always lead to your best work. The fear can be your compass, it can set you on the right path and actually improve the quality of what you do.
Listen to your fear but don't obey it.