Recently, a highly upvoted post in this subreddit rejected a poster's assertion that an invasion of Japan would have been less bloody then the atomic bombings which ultimately did end the war.

This assertion is correct and is not the point of this post. The badhistory sin which that post is guilty of is one which I see come up often in this debate: the omission of the third option for ending the war with Japan; namely, the continued blockade of the non-self sufficient, island nation.

The following is an excerpt from a site which has collected the views of the vast majority of the leading military men at the time on the necessity of the atomic bombing:

In his "third person" autobiography (co-authored with Walter Muir Whitehill) the commander in chief of the U.S. Fleet and chief of Naval Operations, Ernest J. King, stated:

"The President in giving his approval for these [atomic] attacks appeared to believe that many thousands of American troops would be killed in invading Japan, and in this he was entirely correct; but King felt, as he had pointed out many times, that the dilemma was an unnecessary one, for had we been willing to wait, the effective naval blockade would, in the course of time, have starved the Japanese into submission through lack of oil, rice, medicines, and other essential materials. (See p. 327, Chapter 26)"

There are a wide variety of other military leaders listed there with their condemnations of the bombings, presumably based on a similar view on what the correct course of action should be.

Admiral William D. Leahy, the highest ranking "true" military official during World War 2 (i.e. outside of the president, who is its civilian head), minced few words:

[T]he use of this barbarous weapon at Hiroshima and Nagasaki was of no material assistance in our war against Japan. The Japanese were already defeated and ready to surrender. . . .

[I]n being the first to use it, we . . . adopted an ethical standard common to the barbarians of the Dark Ages. I was not taught to make war in that fashion, and wars cannot be won by destroying women and children. (See p. 3, Introduction)

http://www.colorado.edu/AmStudies/lewis/2010/atomicdec.htm

The number of high ranking military officials who condemned the bombing is stunning, to the point where I have double checked the list many times to check its accuracy (despite it being an edu address and assembled by a professor). Everytime it has proven accurate, and the conclusions to draw are pretty clear:

The atomic bombing was not conducted out of military necessity. It was conducted out of political necessity or expediency, which is itself a different debate. I haven't looked into this, but you likely know the theories as to why it was dropped: a combination of wanting to test the bomb, send a message to the Soviets, secure a surrender exclusively to the US, and not to the Soviets as well, or even to end the war before it became unpopular and hurt Truman's re-election chances.

The true reason(s) as to why the bomb was dropped may never be clear. What is clear, however, is that they were not a militarily necessary decision, as related to us by the most qualified and informed military leaders of the war.