I almost never use crayons for artwork anymore, despite having a good-sized collection of them. Last year, I pared down my giant crayon stash and got rid of all of the terrible ones. For as rarely as I use crayons and for as many Crayolas as I own, I don't need what are essentially wickless candles pretending to be art supplies.
I am more of a crafter than an artist, but I'm increasingly realizing that a person will never improve much as an artist if they keep using low-quality art supplies. That said, there are times when you're stuck with using low-quality art supplies. I was recently at an event that had coloring pages and "crayons" (sticks of wax with very little pigment) for the kids. Since there was no rule that you had to be a kid to color, I took some. (My philosophy is that since there's no reason I can't be a Junior Ranger at age 50, there shouldn't be any age-related prohibition on coloring either.)
My box of "crayons" had six colors: red, orange, yellow, green, blue, and purple. No black, brown, or white, unfortunately. I did my best to use varying amounts of pressure to create shades and the illusion of shadows. When blending colors didn't work, I layered them after using my fingernail to scrape off the bits of wax the first layer left behind.
It's no masterpiece. If I'd used Crayola crayons (or better yet, colored pencils) on higher quality paper, my resulting artwork would look a lot better. But it's not terrible, either. Of course, I know there are artists with a lot more skill than I have who could have made something much better with the same materials I did use. The best results come from the combination of practice and high-quality materials.
If you find your skills are not progressing despite practice, it might be time to invest in better quality stuff. You don't need to jump from all the way from restaurant freebies to professional-grade, but it might be worth getting something toward the higher end. My favorite place to get good quality art supplies is Blick. Everything they sell is decent, and you can find good options no matter what your price point is.