Nagasaki and Hiroshima were very different from carpet bombing. Furthermore the UK, USA, and USSR had just beaten Germany into the dirt, and Germany was a much stronger country than Japan. So Japan was at war with those three, as well as France, China, the Netherlands, Australia, Canada etc. with no fleet. They were bound to surrender anyway. I wouldn’t argue that they would have surrendered with or without the bombs, but they couldn’t long resist a landing in Japan itself. All examples of conventional air forces attempting to bomb their enemies into submission have been failures. The Spanish Nationalists could not do it to the Spanish Republicans, the Germans could not to it to the British, and the British and Americans could not do it to the Germans. Other examples would include Vietnam, where the US dropped more bombs than they did on Germany, and they still lost the war. It’s not as decisive as it’s made out to be. As for sieges, that’s a very different operation, where the intention was to take physical possession of a given location, whether it be a proper fortress or a fortified town. In carpet bombing the hope is that you can force a capitulation without needing to occupy the enemy’s territory. Besides, in Medieval Wars objectives were very limited, the entire overthrow of your adversary was practically impossible, so a well conducted siege might get you some small concessions. Carpet bombing would imply you desire the total destruction of your enemy’s war making capacity, which was simply an unattainable goal in previous centuries. Even much later than Medieval times, heck, in the 9 Years War France alone withstood all the other Great Powers of Europe and neither side achieved hardly anything.
Well Grant defeated the main Confederate Army, and his victory at Vicksburg cut the Confederacy in two. A brilliant achievement militarily. Anyhow, the purpose of the Army (defined by Clausewitz, who attributed the idea to Napoleon) is to destroy your enemy’s ability to prosecute war, i.e. defeating them in the field. If they still have an army they will not surrender, no matter how much terror you cause.