I'm not fully decided on the question of the atomic bombings of Japan but I think I qualify as one of the people you refer to. I do not think they should have been used in subsequent wars.

First, the war against Japan and Germany was about as close to an unambiguous fight against evil as you can find in the real world. The post, while trying to paint them as unrealistic caricatures, still manages to understate it. Ultimately, the war was justifiable and winning it was the best outcome for everybody.

If we accept that the war had to be won, then winning it in the most efficient way possible, in terms of time and lives, is best. I think the atomic bombings accomplished that. It's debatable and can probably never be known for sure, but it seems likely that Japan would have held out much longer without them. Even with them, there was a nearly successful palace coup aimed at preventing the surrender. Even ignoring the Allied lives that would be lost in an invasion, many more Japanese would have died by the time the war was over.

That establishes the (fairly standard) reasoning for using the atomic bombs on Japan. How about afterwards?

None of the subsequent hot wars were anywhere close to being as black and white. The post mentions Vietnam as an example where the lack of atomic weapons made for a glaring plot hole. But really, are you going to use atomic weapons on a country that poses no threat to you whatsoever, in a conflict which is basically a war of independence where you're fighting on the side of the colonial oppressors? I'm not going to argue that Communism was a good thing for Vietnam or that victory by North Vietnam was a good outcome, but it doesn't look like our side was particularly in the right. Would lives have been saved by nuking Hanoi? Would evil have been defeated? I don't think so.

And even ignoring all that, the practical realities of the world order prevented it. Maybe you could win Vietnam by nuking Hanoi (although I'm not sure how the one follows from the other exactly) but it's hard to see a scenario where that doesn't quickly turn into an all-out nuclear war between the superpowers, where nobody wins and everybody loses big. The only time it was remotely feasible was for a few years after 1945 until the Russians had enough nuclear capability to make it an unwise choice, roughly 1955 or so. What does that leave us with, using nukes in Korea like MacArthur wanted to? I don't know if that wins the war either. (Mao was famously welcoming of nuclear war, believing that China's massive population meant they would weather it and win it.) And even if it did, would it be worth it? I don't see the balance of lives working out in favor of dropping a hydrogen bomb on Beijing the way it did with Japan.

One more thing to consider: if WWII had been won without nuclear weapons (either because the choice was made not to use them, or the project took a little longer than it did in reality) then my guess is that we wouldn't have seen the subsequent restraint in using them afterwards. Rather than the first (and so far only) use in war being two small bombs, it might have been an exchange of hundreds, with the participants realizing what a terrible idea that is only too late. This has no bearing on justifying the decision in 1945 (how could they be expected to know all these future consequences?) but it's interesting to consider that the timing of the development and use of nuclear weapons may have been extremely lucky.