When teaching a class on how to draw animals, we covered mostly graphite and colored pencils, but one of my students wanted to draw with crayons. It was fun cracking open the box of Crayolas and giving the class a demonstration. I shared the illustrations I had done for the book, and we analyzed the characteristics of drawing with crayons.
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.