I'm not going to debate whether it was justified or not, whether it was moral or not, or whether it hastened an end to the war or not. That's for scholars and historians far more educated and informed than myself.
What I will say is that since that time, there has not been a single nuclear weapon launched in anger at an opposing force, even though there have been numerous times where such a course of action was considered.
Hundreds of thousands of Japanese lost their lives when we dropped "the bomb" on their country. Yet those two bombs (Little Boy and Fat Man) were comparatively tiny when seen in perspective. Little Boy, the one that destroyed Hiroshima, had an estimated blast yield of about 15,000 tons of TNT. Fat Man, the Nagasaki bomb, yielded just over 21,000 tons. That's a lot of power packed into a single weapon, but within a few years those yields skyrocketed into the MILLIONS of tons of TNT. Less than nine years later, in March, 1954, the US set off what would end up being larger than any other tested weapon in the US arsenal -- over 15 megatons. That single weapon, in an single instant, had over 1000 times the devastating power of Little Boy.
Wars continue to occur, and many nuclear nations have arisen over the decades. But not even openly hostile and angry confrontations between centuries-old enemies have persuaded the generals and national leaders to open the nuclear genie bottle again. I don't think it's coincidental that the horrors and devastation wrought by those two war-fired weapons have impacted the decisionmaking of countless nations, and that fact alone has probably saved many, many millions of lives from absolute destruction by nuclear fire.
Don't ever forget. War is hell.