In addition to all of those motivations, I guess, it was the expression of the era trend of thoughts those days. It was just before they got into the era of total war. They have had to endure the pain and agony of total war twice very soon. As artists sensitive to the trend those days, they must have felt that era preceding to the other people. In late romantic music, there used to be such a composer who had preempted that trend of anxiety and fear for the death. One example was Mahler. But such attempt by late romantic composers has not succeeded in it and was followed by the modern music composers, who have done thoroughly, if it was successful or not.
This quartet by Schoenberg is deemed the watershed dividing those two eras. Each motifs sound very beautiful with faint feeling of tonality. When the soprano enters in the music, the atonality dominates it. It may express the anxiety of existence in the era trend. It appeals to our mind even after over a century since it has been composed.