This is a great question. The context in which something is written makes a huge difference. Let me give you three reasons for this point.
First, if the letter were written from a comfortable desk, then some may be tempted to see the words of the letter from a more theoretical point of view. It could be seen as good counsel, but nothing really pressing.
Second, the very fact that the Martin Luther King Jr. is writing from jail says that there is immediacy. What Martin Luther King Jr. writes is completely applicable in the present, because he is in jail for his beliefs. There is nothing theoretical to his words. What he is writing about is actually taking place.
Finally, in the face of suffering and injustices, actions need to take place. To flip things around, Martin Luther King is writing from prison to people sitting in comfortable desks. This incongruity should cause action.