What's the deal with prime lenses

Many people thanked Fuji for listening to enthusiasts when designing the X-pro1 camera. One reason for this was that they released three fast prime lenses rather than just basic zooms.

But tell me, what's all the commotion with prime lenses in general? Yeah, you may get sharp corners, but isn't it MUCH more convenient to shoot with zoom lenses. You get the exact crop you want without moving around and it's a way more convenient not to carry around 2-3 different lenses.  Changing lenses takes time and can be even risky sometimes as you can damage the lens / sensor.

I don't think it's an image quality issue either as there are very good zoom lenses available. Even though they are expensive, you probably still save money compared to buying 2-3 different primes.

So be honest. What's the point with prime lenses? Are they just for pixel peeping or photography elitists and rest of us can benefit from the convenience of zoom lenses?