Without the bomb, there would be an invasion.
The invasions of Okinawa and Iwo Jima were previews of the invasion of the mainland. American casualties would be extremely high, as would Japanese casualties.
The bomb saved lives.
Oh, the last battle (Okinawa) is the one that led several to revise their earlier casualty estimates of a mainland invasion. One of which placed the Allied losses at around 1 million casualties. And Japanese losses at well over 6 million dead. And yes, I am being very specific here, as was the report. Allies at around 1 million casualties (dead and wounded), and Japan with over 6 million dead.
And even more telling than the 2 you mentioned are 2 earlier battles.
At the Battle of Tarawa, where 35,000 Marines landed on an island occupied by 2,600 Japanese. Now this is the first major battle between the two forces, so remember that the extreme hatred towards the Japanese soldiers had yet to develop which led to "no surrender" orders because of their tendency to attempt to give false surrenders just so they could try to kill more before dying.
Of those over 2,600 Japanese soldiers, only 17 were captures alive. And almost all of those were badly wounded when captured so could not resist.
And now we will fast-forward to the Battle of Saipan. This was the only island we had to invade with a significant Japanese civilian presence (Okinawa is a Japanese prefecture, but culturally they are very different). This is the island where over 7,000 civilians killed themselves, many on film. There is plentiful footage of crying American translators trying to talk entire families into surrendering as they climbed the cliffs, only to see the parents throw their children off of it, then jump themselves.
Of the over 25,000 civilian population on the island prior to the invasion, only around 1,000 survived the battle. Suicides were rampant, along with civilians attacking with knives, spears, and hand grenades. And this was a true "Japanese Civilian population", Japan had only had control of the island since 1919 when it was turned over to them from Germany after WWI. And for almost 2 decades they made colonizing it with Japanese citizens from the mainland a major part of their overseas strategy.
This is what by the middle of 1945 those who knew and understood Japan were trying to get the US government to understand. Not even Mac really understood this. Yes, he was undoubtedly an "Asian Expert", but that experience was based on his understanding of Chinese and Pilipino cultures, not Japanese. And anybody that does not understand that there are vast differences in them is either a fool, a liar, or both.
And this lasted for long after the war. On Okinawa, most of the civilian casualties were actually inflicted purposefully by the Japanese soldiers. They knew that the Okinawans were "culturally different", even to this day their "popular media" presentation of them is generally of a simple, backwards people who are not very bright, have no real warrior spirit, and love only Watermelon and Turtles. A simple, carefree people who love to wear little to no clothes and do not have a care in the world. Where a depiction of a "Mecha" in Japan is always a fighting robot like Voltron, if such is in Okinawa it is always a mechanical turtle.
The depiction of an Okinawan is generally like that of an "American Redneck". Akin to wearing a tank top, mullet, leaning on a broken down truck. Rustic, simple peasants and in general looked down on.
A large difference between that, and the warrior mentality of the mainland, especially in the early Showa era.
This is why so many were slaughtered by their own country, the soldiers knew that if given a chance they would surrender, so they killed them so they would not dishonor themselves. When I lived on Okinawa, we had to be very careful when talking to those old enough to survive the war. Never to
ever refer to them as "Japanese", they were "Okinawans". Most of the survivors of that battle had a lifelong hatred of the "Japanese". And in fact, while we could go anywhere we wanted on the island, the Japanese military who were stationed there were confined to their bases. Still not allowed to leave them, even 45 years after the end of the war.
This is the difference between somebody that only knows of Japan and the war from reading revisionist history, and somebody that has actually lived there, and knows and understands enough of the culture to recognize things like this.