Chaotic about method but not chaotic about goals.
Commanding officer gets shot? Alright, time for a battlefield promotion. Now that grunt doing the leading doesn't have any West Point training but he's got a goal, he's got men and guns, and he'll find a way to achieve it. Might not be the "right" way but if it gets done then who would fucking complain?
This is what top-down, conscription-based (or conscription-lite like... anywhere in the mid-east where officers are a different breed entirely from the grunts) armies cannot do. Now this doesn't mean the US is more protective of grunts or anything, we still send them to die in the thousands. But we also don't assume that they're ALL gasoline-chugging retards; if only grunts are available then they WILL be running the show in a US campaign. That doesn't happen for China or Iran or Venezuela or Russia.