Peaceful protests are one thing - but how many riots were there in the South.....
Not necessary comparing the two - other than to say that instead of protest marches - why didn't Martin King just - well as in your words There is a whole system of law in place to address the grievances (post #9 ). King simply could have went to court to change the laws.
They aren't mutually exclusive. You can challenge through the courts and peacefully protest. That is what was done. Protests happened while at the same time, laws were challenged in court.
To bring things somewhat full circle, Washington didn't have protesting or legal challenges as any real viable option.