I think this is a pretty rose-tinted look with hindsight bias. The USSR was pretty driven to be "the best" right up to their demise. North Korea existed for half a century because China intervened in the Korean War and MacArthur's warmongering got him ousted, not nuclear deterrence. Finally, the idea of a "city-wiping bomb the size of a suitcase" was well understood by all nations with advanced physicists, not just the US: so the Nazi regime was also very close to having a completed nuclear bomb.