Many believe it was necessary to drop these bombs because otherwise we actually may have had to invade Japan for them to surrender. This would have lead to untold casualties on both sides. /QUOTE]
This is what I believe.
Based on the fighting on Okinawa, it became clear that we would have to fight for every inch of ground on Japan, and would have had to take all of it, fighting almost every single inhabitant - potentially killing most of them.
The bombings made it clear - we can, and will, kill every last person on Japan. We will do it from 20,000ft with relative omnipotence. You will die unable to fight back. Or you could surrender.
Our victory over Japan was as absolute as it could be. To this day there are more American military personnel in Japan than Japaneses military personnel. We re-wrote their constitution that still blocks them from having much of a military at all.