Well to answer one of your questions – surely it WAS a deterrent for the Soviet Union – just as Soviet nukes were for the west?
That was the whole argument of Mutually Assured Destruction.

The difficulty with this argument is that the United States was already providing a comprehensive deterrent against potential Soviet aggression in the form of both conventional and nuclear forces, to which the UK’s nukes constituted a trifling addition.

Indeed, in the real world we know that the British nuclear program, far from being a manifestation of the Special Relationship™ as claimed by Carter, was in fact driven by the desire to maintain Britain’s independence from the United States and its security guarantees. This may have been (and may be) an entirely sensible objective, but it is not one that allows or helps the UK to “play an outsize role on the global stage” — it merely ensures that the UK remains on the stage and able to function as an independent actor.

I would also wager that after the Black Buck raids and the sinking of the Belgrano, the Argentinian Junta were suddenly very mindful of the UK’s nuclear capability – especially as it was Mrs T’s finger hovering over the button.

Surely the risk of nuclear attack for Argentina was not when they were already reeling from the imposition of British power (non-nuclear, you may note) but rather in the event that they succeeded in repelling the British counter-attack and/or sinking much of the task force? In this context the function of nuclear weapons (directed at, one assumes, Beunos Aires, or the Falklands themselves, or both) would be to deny Argentina victory and salvage British pride.

And today? Well I bet fat Kim in North Korea knows exactly who has, and doesn’t have such a capability

I’m sure he does, but not for the reasons you imagine. Undoubtedly the North Korean leadership has observed that neither the United States nor anyone else has ever threatened the survival of a nuclear-armed nation. Indeed, this points to the real utility of nuclear weapons as being most useful for weak states that, in the presence of a credible threat, are unable to guarantee their security by conventional means: North Korea, Iran, Israel, Pakistan, perhaps India. Paradoxically, it is the Big Five nuclear powers — those with the most comprehensive nuclear arsenals — that are today least in need of nuclear weapons.

I suppose the question back would be – would you feel safer NOT having a nuclear capability?

Well, I live in a country that lacks a nuclear capability, and I’m pretty comfortable with that. Certainly if Australia were to choose to develop nuclear weapons, I don’t believe I would either feel safer or be safer as a result.