The importance of having a properly fit bicycle not only is for injury prevention, but it's also for performance improvement. Competitive cyclists, having the bike fit properly helps with the overall performance. It will also help with their aerodynamics and then that all improves their performance then also.
Injury or aches and pains that a cyclists would get would be low back pain. That is pretty much due to the seat and the handlebars, them leaning too far forward, but also, not having the flexibility in their hips. Some good stretches that would help with that would be hamstring stretches or a double knee to chest kind of stretch to stretch out your low back.