Stage fright plagues many performers: musicians, public speakers, singers, actors, etc. etc. (In fact, we could experience 'stage fright' in any daily activities that bring us discomfort. Think of what happens to you when you are nervous: dry mouth, butterflies, shaking, nausea, sweaty palms, etc.)
Many in the arts believe stage fright to be a taboo topic and one that prepared performers should not experience.
This New Yorker article takes a closer look at the inevitable fear of performing and lists some of the great musicians of past and current times who experience(d) terrible stage fright.
Stage fright is very common and a topic that all teachers should openly discuss with their students. Coming up with strategies to handle it (in addition to solid preparation) is the only way to defeat it!