Development and improvement of nuclear weapons was an entirely American project until the technology was exfiltrated and then it became an instant arms race. That cat is already out of the bag with LLMs. Distillation is just the fastest way to keep pace but that in no way prevents other countries and actors from doing it the hard way.
An arms race doesn’t imply one side winning, it’s not a race with an end goal, it’s a race to keep pace or retake the lead position which can oscillate between the parties involved indefinitely. The other option is to agree to make no further progress or to disarm.
There were prominent scientists like Oppenheimer who did not think it needed to become an arms race, and campaigned against that. But there were others like Teller and the military who made it into an arms race, and kept upping the ante with more powerful nukes.
Point being humans make theses decisions. It's not an inevitability.
>an entirely American project until the technology was exfiltrated
No it wasn't. https://en.wikipedia.org/wiki/Tube_Alloys
Post WW2 the USA (for a bunch of quite interesting reasons) excluded the British. But, of course, the British had acquired a lot of knowledge from the program and were able to develop their own bomb.