standing in front of the smouldering ruins of Constantinople, flaming torch still in hand.

"Why would Islam do this?"

I would posit the 4th crusade was the successful one. Yeah the crusaders ran out of money and just pillaged Constantinople instead of doing another doomed attack on Jerusalem. People actually managed to get rich and dip in this crusade. Yeah Jerusalem is sill controlled by the Saracen, but I imagine for most of the nobles in charge that was just an excuse to go kill people and take their stuff. (I simplified this all a lot but still)