The Japanese had plenty of warning, you think they didn't know the US had a big ****ing bomb after the US tested Trinity? Any thought of dropping it in a relatively uninhabited area would be showing the Japanese something they already knew. As the OP mentioned the Japanese would have fought down to the last man, women, and child. The Japanese people were told that the Americans would torture them if they were caught, so many preferred to commit suicide which is deeply ingrained in their culture and viewed as acceptable.
In fact, when the Emperor decided to surrender, a group of generals made a power play to try and kill the Emperor and seize the government and keep fighting. This is after not one but two atomic bombs were dropped on the Japanese Main islands and the firebombing of all the major cities in Japan. The US had a couple more implosion type A-bombs and if after 3 days of Nagasaki they got no surrender they would be ready to place a third bomb on Tokyo. So as you can see things could have gotten a lot worse.
Any siege or peace agreement that could have been signed without the bombs, would require the Soviets who the Japanese were more comfortable to surrender to. As we all know the Soviets have a habit of not leaving a country once they entered and turning the government communist. The US already had to deal with Eastern Europe being lost, and China wasn't looking good for the Nationalists. By dropping the bombs they were able to achieve unconditional surrender without the Soviets and they sent a message to the USSR that we had a big bomb and we weren't afraid to use it. I do agree there was a kind of revenge factor of "They attacked Pearl Harbor, we're gonna make them hurt too." This is the normal not in my backyard mentality, which is pretty much unavoidable with a company as nationalistic as the US.
I do not mean to minimize the significance of all the victims though. Many people lost their lives, and those who did survive lost loved ones, their belongings, their lively hood, and had their health negatively affected. The Bomb killed tens of thousands of people instantly, even more died in the ensuing fires which turned most of the town into a raging inferno, still more were killed by the fallout and radiation sickness. I believe by reading the book Hiroshima one is able to understand how greatly the people of Hiroshima (and indirectly Nagasaki) were affected by this cataclysmic event. Even when I consider the victim's stories I still think it was necessary to drop the "Little Boy" on Hiroshima and since this didn't seem to have enough of an effect on the government, the dropping of the "Fat Man" on Nagasaki was also necessary. Although I do concede that It may not have been completely necessary as the "Little Boy" may have been enough if enough time was given, but the "Fat Man" precipitated the unconditional surrender of Japan.
Note:
*The "Little Boy" was the codename of the gun barrel typed nuclear device utilizing which utilized Uranium 235
*The "Fat Man" was the codename of the implosion type nuclear device which used Plutonium.