Inevitable? no, you can never tell what leaders will do. Ever.
It
might have led to an exchange between two nuclear armed countries, likely the US and the USSR in the 50s, maybe. But who knows? Maybe the non-use would have allowed the US to build up a decent stockpile, obliterate some small, annoying country (North Korea or Cuba perhaps) and become an international pariah, having committed a genocide never seen before.
or maybe, the space aliens that never have shown themselves in the Real World show up and make us into their lunch meats, because we didn't have atomic weapons to defend ourselves in the numbers that they truly fear.
Or maybe the Russians develop WAY more nukes than the US does (Like 30 or so) by the early 50s, and uses them to blackmail the US into leaving Europe, and then the USSR slowly takes over the NATO countries by covert and not so covert means, as the US descends into McCarthyism Times 1000 Paranoia. Canada becomes the new DMZ.
Or, maybe the UK and France team up to make nukes along with the rest of the Western Europeans, as the US isn't there with boatloads of them. Proliferation spreads nukes to almost every country and we achieve true peace due to MAD being complete and total. Both the USSR and the US return to their agricultural roots, and we now today live in a world of fields and waving grain crops, and NO INTERNET!!!!!! OMG!!!!
Or maybe the US decides to show the world excatly how bad the nukes can be after a long, terrible and bloody campaign to take the Japanese home islands, and blows Tokyo off the face of the Earth in a series of "tests". Worldwide opinion is one of horror, quickly escalating to sheer horror when the last and most powerful tests awakens a giant lizard, that proceeds to stomp pretty much everything flat in it's path, even Raymond Burr.
or, little Jimmy wakes up screaming, realising the atomic bomb in the pit was just a dream, and there are no Martians pretending to be his parents.
It's "What-if", not "For Sure". We'll never know for sure.
Alvis 3.1