If you read newspapers and magazines from the time, the bombing of Hiroshima was considered as something fundamentally different from greater horrors, in terms of loss of life, like the firebombing of Tokyo. It took just one plane and one bomb to destroy a city, and people died from radiation long after the event.
The military tried to keep the details of the damage secret, and we can thank John Hersey for letting us see the impact.
It is no accident that there were tons of after the atomic war, end of the world novels in the late '40s and early '50s, and beyond.
As for the OP, I agree with just about everyone that there would be another war.
I agree it would have been very bloody, but I think the western powers would have still emerged with a complete victory. With regards to comparisons to the Korean War, that ended up as a stalemate because the Chinese got involved once the US forces got the upper hand against the North Koreans. That’s what led to the negotiated peace. In a world without nukes, the incentives on both sides to stop at the 38th parallel (along with avoiding many other wars that would likely have started on many different fronts) wouldn’t have been nearly as strong. In a WWIII scenario, the Soviet and Chinese forces would eventually be overwhelmed because of having to fight on too many different fronts. They would have to defend against attacks across the English Channel, attacks from Spain into France, attacks from Northern Africa across the Mediterranean, attacks from the the Middle East going north through Georgia, attacks from India going northward, attacks from Korea into eastern China and Russia, attacks out of Japan, attacks from Taiwan, the Philippines, and Australia into southeast China, and attacks across the Arctic from Canada and Alaska. I doubt that the Soviets + China would have been able to hold out for more than a few years under those circumstances. Assuming the western powers perceived the war as an existential threat, they would be unlikely to let Stalin and Mao have all of mainland Europe, Asia, and Africa in exchange for peace.
While it is true that we have not had a ‘world war’ post-1945 in the sense of ‘Great Powers’ facing off against one another on a battlefield, the latter half of the 20th Century had plenty of conflict, and just because it was happening in places no one really cared about doesn’t mean it wasn’t widespread and horrific. It is a commonly-repeated factoid that the US dropped more tonnage of bombs (estimates of 7 million tons) on Vietnam during that conflict than in the entire European theatre during WWII (2 million), but it seems to be less known that we dropped the same tonnage of bombs on Laos as in Europe in a ‘secret war’ that was not acknowledged for decades and has left Laos not only with the title of “Most Bombed Nation Per Capita on Earth” but also with still over half a million tons of UXO, with explosives still routinely killing and maiming people and ordnance removal one of the biggest industries in the country.
As for the 21st Century, the US alone has launched the two longest wars in modern history, essentially destroying the complete infrastructure of Iraq and leaving it vulnerable to religious fantasists, and following the experience of the Soviets by engaging in a pointless conflict in Afghanistan despite the common wisdom about not getting involved in a land war in Asia. China has long supported the separation of the Korean Peninsula, and the general shit-stirring of the Soviet Union around the globe has certainly racked up plenty of bodies outside of their own home-grown famines and massacres. Color me unimpressed for what “nuclear weapons and MAD” have done for peace, notwithstanding the fact that most people have no real understanding of the precepts and assumptions of the deterrence strategy of Assured Destruction and the logical arguments for why it doesn’t actually apply to the real world.