I think the biggest problem people have when drawing with crayons is that they regress to being five years old again. They hold the crayon like they're coloring again, instead of applying it like a fine art medium. Another problem is that many people want to make it perform like colored pencils. While similar in application, they are quite different. You should not use crayons and expect them to behave like colored pencils. You'll be setting yourself up for disappointment.
A Variety of Pressure Creates Emphasis. If there are some areas you want to accent, you can press a little harder on the crayon and end up with a darker, more intense color. This is another good reason to color lightly for full coverage. For example, in this picture of the heart below, I pressed harder when tracing the lines within the heart and in the vein and artery openings. I did the same thing when coloring the muscles and the brain.