MLK didn't ask to be the leader of the Civil Rights movement. It was a responsibility thrust upon him because he was so good at articulating grievances. It was like, he woke up one morning during the Montgomery bus boycott and all of sudden he was its leader!
He did not have time to map out a precise strategy or a long range grand plan, he and his cobbleled-together posse just kinda made it up as they went along, with Mahatma Gandhi's nonviolent philosophy as their inspiration. The idea of making a lot of long-range, multi-faceted demands was out of the question at that time. The movement just focused mainly on equal opportunities, and King endeavored to appeal to the conscience of his oppressors.
Integration was a counter to the separate but equal policy that was nothing more than subtle Jim Crowism. Integration represented fellowship and harmony where little black boys and girls would join hands with their white counterparts and partake of equality through tolerance. It was a dream; hence King's "I have a dream" speech.
In hindsight, it's easy to criticize him for not embracing the militancy of those like Malcom X and the Black Panthers. But MLK was a man of his times and he was just beginning to re-think his goals when he was assassinated.
Many think his taking a stance against the Vietnam war was a mistake but his doing so was in keeping with his pacifism.
A cigarette-smoking, scotch- drinking, womanizing King was not perfect, but he fought the good fight, and paved the way for those who eventually came to criticize him for not having more foresight.
I lived through King's era, and to me and my contemporaries, he was a real live hero who died a martyr.