Crawling is one of my favorite drills.
I use it in the block zero program as a staple movement to teach core stability and control during alternating reciprocal motion of the arms and legs. Which is very much like walking, except that in the quadruped position it is much easier to maintain the neutral spinal position than when you are upright and forced to battle gravity with only two points of contact on the ground. Another great thing that you get from crawling is good motion of the scapulae with your hands on the ground. Your hands being on the ground increases the proprioceptive input and subsequently your kinesthetic awareness.
In the beginning phase of training (block zero) crawling is built into the program that naturally builds from the ground up. Everyday we start on the floor in a 90/90, or supported supine position. This position is the best for learning proper breathing patterns, which we know to be the keystone to good movement, health, and longevity. From there we work ourselves into some rolling drills and start to increase the demand for core strength and control. If you haven’t tried this rolling drill, then you need to. AND IF YOU CAN’T DO IT PROPERLY WITH YOUR ELBOW TOUCHING YOUR KNEE THEN YOU SHOULD DO IT DAILY UNTIL YOU CAN. Don’t worry, it won’t take that long to progress.
Once the rolling drill is mastered, we get to the crawling drills. When starting in block zero with my kids at school we spend a large chunk of out practices for the first couple of weeks in the quadruped position. Drilling moving while breathing and maintaining our hip position pays in dividends once we get into the meat and potatoes of our program.
As with most anything, pay attention to the details. Crawling around your gym and not doing it perfectly is pointless.
Crawling, like most block zero movements, should really never go away completely. Doing a little crawling in your warmup or cool down a few times per week can be really beneficial to help you prime good movement patterns prior to your training, or can help you reset yourself after a tough squatting or pulling session when you will inevitably leave you with a little excess extension. Adding some implements can also make a crawling drill some effective low intensity conditioning work.