No...stage fright also affects experienced speakers. The key with dealing with any fear or phobia is to keep exposing yourself to your fear...also known as "facing your fears". If you avoid your fears, then you never get to find out that your thoughts about the feared situation is not that bad. So when you continue to give talks repeatedly over time, you gain confidence, your anxiety lessens, and you may eventually come to enjoy talking in front of an audience.
So the solution for speakers who have stage fright is to continue doing what they are fearful of...to continue giving talks in front of an audience. And this solution is something experienced speakers with stage fright know quite well.
The following video explains how stage fright develops, and what you can do to address it:
