PragerU gives an argument for why the atomic bombs should have been dropped on Japan. How valid is their argument?

Without having the time to go over things point by point, I would just say, the main problem with this form of argument is that it limits the number of alternatives to a very small number, notably "full land invasion of Japan by the USA" versus "drop two atomic bombs on two cities." If you constrain the possible choices to those two, then yes, it is very easy to conclude, as he does, that the dropping of the atomic bombs was the lesser of two evils, especially if you let your imagination run rampant as to how terrible the invasion would be (the figures he quotes are much higher than any estimates that were made at the time; that is not to say they are wrong, but they are not the figures that may or may not have influenced the decisions being made). There were many other alternatives being floated at the time, and bringing those in complicates the calculus considerably.

Separately, he seems to give full credit to the atomic bombings to causing Japan's shift to surrender. Historians debate this matter considerably. It is not at all clear that the atomic bombings were what caused Hirohito to make his intervention; the simultaneous invasion of Manchuria by the USSR seems to have had a great effect as well. Adding these sorts of factors into the consideration again diminishes the "special" role of the bombs in the overall calculus, which again causes one to question whether the specific scenario that occurred was truly the best of all alternatives. For example: even if one credits the Hiroshima bomb with applying some pressure (which many do, even those who do not think it was enough pressure by itself) along with the Soviet invasion, was the second bomb necessary? There is considerable reason to think not: the Japanese attitudes towards the war do not have seem to have been affected by it, having already been "set" prior to their learning about it. "Was it wrong to move the Nagasaki bombing date up so soon after the Hiroshima bomb?" is a separate question than he is asking, but if you are doing a real moral accounting of history (which is his stated goal, not mine), then that's part of it.

Lastly, he frames the historiographical dispute in a way that reflects very old scholarship — I suspect he has not re-examined these questions since the mid-1990s. There have been two primary "historical schools of thought" on the bomb, what we might call the "orthodox" one (put forward in 1947 by people involved with the atomic bombing work) which is what he is advocating ("Truman had to make a tough decision and this was the best of the two options") and the "revisionist" one (which first arose around 1949 but has been revived in variations in the 1960s, 1980s, and 1990s), which argues that the bombs were just power-plays in the new Cold War and that everyone at the time knew they were unnecessary.

Historians who study this today tend to reject both of these approaches as being incorrect to various degrees. There is a synthesis of the two which recognizes that a) there was no "big decision", b) people have mixtures of motivations, and c) history is messy as hell and doesn't fall into neat moral stories. (See J. Samuel Walker's essay from 2005 on this, which still holds up well.) What the YouTube video does is basically do a full-throated endorsement of the partially-debunked "orthodox" view, while making very minor acknowledgment of the "revisionist" view. Again, it doesn't represent the actual options out there — it picks one extreme, then pivots to the other. So it doesn't really represent in my mind how historians who actually work on this stuff actively today think about it (I say, as someone who works on this actively today). It is more soapbox than historical discussion.

Granted, it is only 5 minutes long, and this is a subject that can be talked about at length. But since it is going to make such a clear to how "unambiguous" the judgment is, I would point out that many, many, many historians, and many people of the cloth (for what that is worth), find it far more "ambiguous" than he makes it out to be.

I can also not help but point out, since he wears the collar, that he does not at all address the core moral question at the heart of the bombing, separate from the historical ones: under what conditions are nations permitted to deliberately massacre non-combatants by the hundreds of thousands? If the answer is simply, "if we imagine it would have saved lives in the long run, against our worst fears of the alternatives," I am sure he recognizes that this creates some very problematic possibilities moving forward.