The most common misconception about the CM method is that when people see the "monkey" stance they think that the practicioners stand like that ALL THE TIME, from the opening bell. That is very far from the truth and one of the things Rodney King stresses at the beginning. You can use any variety of boxing stances while on the outside and shift to the CM defensive posture only when the punches come in.
It's very small but this gif shows exactly how CM should be used. Notice how Rampage goes to that hand posture as soon as the fists are inbound.
Rodney "Chico" King developed, or more accurately adapted this method of boxing defense because he felt that the dropout rate in his striking classes were very high compared to his grappling classes. He saw that he could teach just about everyone who walked through the door, big or small, strong or weak BJJ but of all of those who started out boxing or kickboxing very few stuck with it to reach a competent level of skill. Before he incorporated grappling into his curriculum he had always just taken it as a given that the majority of people trying their hands at combat sports would wash out. After looking at the situation critically he came to the conclusion that traditional methods of teaching striking arts were very much attribute-based - if you didn't have a fair chin, natural agressiveness enough speed and hand-eye coordination, and a willingness to get hit in sparring it would be very hard for you to make any real progress at a beginner. On the other hand BJJ was technique-based and thus didn't demand as much natural inclination for the pursuit.
The CM posture is for those peeps that want to learn how to strike but don't have the natural attributes to bob and weave or beat people to the punch. With a good blocking method to fall back on people gain confidence that they can spar without getting hit in the face too much or wobble. Some guys continue to use even after they become competent, but you can also see the method as a sort of "training wheels" - as you gain skills and confidence and get used to exchanging strikes you can transition into more diverse ways of not getting hit and counterstriking.
That's basically why Rodney developed his version of this stance. Please note that he has never tried to take credit for inventing it out of thin air, variations of this type of defense have been around in boxing (and probably Muay Thai too) for a long time under a variety of names. Some people refer to it as The Wall, others just see it as a modified version of the peekaboo defense. Rodney just adapted it to MMA and self-defense.