Q: Why such a big deal about stepping?
A: The fundamental history of martial arts is about battlefield activity not street fighting. Falling was not something you wanted to do. In some cases you were not allowed the luxury of going to the ground.
Q: Why is everything so formalized?
A: Every art has its basics. Give full contact a few more years and people will be starting with similar patterns. Let me remind you that not every style starts with steps. Some start with movement. Three I can name are PiGua, Bagua and—big surprise—original Okinawan Karate.
Q: What are the key points to remember in general?
A: Regardless of the method of your stepping some points remain. Don't be off balance, especially to the front. Try to keep the spine erect as you move. Touch with the foot then grab the floor. Be natural. Move from the core. See, there's nothing there that's all that strange.
Q: Anything else?
A: Yes, for the sake of honesty I have to mention some obscure areas that influence formal martial stepping. First is the connection to cultural dance, particularly in the case of the straight sword. Second, is the influence of Chinese instructional methods in the written language. The paradigm is: first you learn the strokes, then the order, then the cursive script; stepping is taught in the same order mostly. Lastly, and frankly, some people can barely move and much stepping is just to encourage their locomotion. So a lot of stepping, to be honest, is influenced to some degree by other concerns: cultural and historical. The point is that the KEY issue, mobility, should always be kept in mind and you won't go far wrong.