This in-show argument never made much sense to me either, tbh. I mean, King's Landing needs to be taken one way or the other, and all of them will be bloody. Hell, dragons could even make keeping civilian casualties low easier. Just take to the air and focus on the Red Keep (which is conveniently facing the sea) in particular. The city proper will be spared, but the enemy head cut off. Alternatively, draw a siege around the city and just burn all relief troops.
I was wondering why they don't just do this. You could have a draconic precision strike right on the Red Keep and then the war is pretty much done.