Solider nor purge could win. This is correct.  Gabriel influences fate itself with his power to make a fatal attack miss. Hence they would be unable to kill vampires at all.

What is stopping Bedivere is simple. It is as he said. War changes nothing. One battle proves nothing. Humanity will survive and fight on at massacre for fear breeds hate which brings rebellion. To crush hope and throw them into despair places them under the yoke. This brings change.

Let's let a GM decide on what should happen.