Rhetorically, it seems like the reason MLK discussed white moderates was because he knew they would be the first white people to warmly accept black civil right

Rhetorically, it seems like the reason MLK discussed white moderates was because he knew they would be the first white people to warmly accept black civil rights, put justice above order, fight for tense peace, and accept an accelerated timeline for freedom. The same principle is why you can say "I expected more from you" to friend or family member and that simple comment spurs an improvement in behavior. They actually care, a little bit at least. We don't eloquently express our lofty expectations when it comes to our enemies. Only our friends, allies, and teammates.