the reason they dropped the bombs was that they wanted absolute surrender. this panel is repeating a widely held misunderstanding: that the japanese were not willing to surrender. in fact, they had already been negotiating a surrender for quite some time. the biggest factor was that the americans had cut off their access to indonesia, which was their source of oil and rubber. the outcome of the war was crystal clear somewhere around d-day, and was in fact understood even earlier than that. the japanese could barely even fight without oil & rubber, let alone win. they had no chance. it was just a matter of time.
but, they didn't want an absolute surrender. the standard line is that they didn't want to hand over the emperor, but that's one of those historical glosses. like the idea that world war one was about an assassination in austria by serbian terrorists, rather than imperial competition over global resources. in actual fact, the japanese wanted to hold on to certain strategic islands, for resource reasons. these negotiations were preventing a surrender.
the actual truth is that the americans would not accept anything less than absolute surrender, including the occupation of all japanese lands. the japanese saw that as a bit onerous. so, they dropped the bomb to try and force the concession. it was a negotiation tactic. and, the fact is that it actually failed - the japanese did not surrender as a consequence of the atomic bomb. this is where the political/military debate comes in - the military knew it wouldn't work, but the politicians pushed for it anyways. that's become a common theme in american imperialism, and is perhaps reflective of somewhat of a flaw in the governing structure of the united states.
so, the bombs had little to do with the surrender. rather, what happened was that the russians saw what was going on and took it upon themselves to move in. this was just strategically intelligent. so long as the japanese and americans were haggling over terms, the japanese were an easy target for further expansion. further, the soviets had reasons to keep the americans out of japan, too. what set in was a race.
the japanese elite now saw themselves in a situation where they had to choose between being taken over by a communist regime and being absorbed by a capitalist empire. the capitalists may reduce them to a puppet-state, but the communists would execute them in public. so, they picked the americans over the soviets and accepted the absolute surrender.
it was the threat of stalin that forced the surrender, not the bombs.
but, that doesn't address the question of whether it was justified or not. i mean, just because it failed doesn't mean it was unjustified. i think this is a complex question without a good answer, but at the very least you need to get the motives right, first. see, you get a very different analysis if you think it was about ending the war early than you do if you understand that it was about forcing absolute surrender.
i think the better argument is that the atomic bombs actually weren't as large of an escalation as has been imagined. these were small bombs, in contemporary terms. the topic of iraq is brought up here. it was widely reported in 2003 that the "bunker busting" bombs - which were conventional - were actually more powerful than the h-bombs that were used in japan. and, the americans dropped depleted uranium in iraq, too.
i've argued both points, depending on context. my reaction has tended to be dependent on the precise argument i'm interfacing with. but, i don't think there's an actual answer.