That would break the no kill policy he has built his reputation on, in addition this might make the general public cease trusting him and perhaps try to detain him which if successful would lead to even more deaths.
Not all people would, especially those who've defended Batman on the basis of his moral superiority. That defense would be more complicated, and some might feel they've been made to look foolish or stripped of the moral foundation for their defense. Their objections might gain momentum.
timzava
