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Nuclear umbrella's are interesting to talk about but I think they're a bluff against any kind of peer power. Washington is not going to get LA, NYC, Dallas, Denver, San Diego, Boston, Washington DC and a hundred other American cities wiped off the map to avenge say Seoul getting nuked or Berlin getting nuked by the DPRK or Russia respectively.

Because nuclear war is hard to do in a limited way between nuclear powers. A nuclear power can nuke a non-nuclear power in a limited way because the non-nuclear power cannot respond with any nukes let alone a full barrage that completely destroys them. But once you hit back at a nuclear power that can wipe you off the map the doctrine states any limited strike is only an attempt to blind you and suppress your response before a full strike, you can't know what is or isn't coming in terms of more so protocol is launch a full response and at that point both parties are destroyed and those do no good to the umbrella party which previously was still intact and spared and could undertake other choices against the attacking party.

Likewise I'd have doubts if China extended a nuclear umbrella to say Iran that they'd be willing to hit the US with a nuke because the US hit Iran.

Certainly the US has a lot more to lose as does France in hitting back a big nuclear power than say China who is still a rising power, still does not have any kind of vassals, whose only interests in security are immediate neighbors like Vietnam/DPRK that they've assisted in the past militarily. But even there I think it would be a hard choice to make watching say the DPRK in flames but knowing if you hit the Americans back that Beijing and every other city in China will be in flames as well.

The US might buy such an umbrella for the DPRK and say Vietnam from China and not hit them but they wouldn't buy it for say Pakistan I think because of the dissimilarities there. Likewise the US probably buys Russia's threats to defend Belarus because well they've backed them into a corner, they know they've backed them into a corner and they have almost nothing left. The US on the other hand and France can stand to lose a lot, they have a lot of countries and/or ocean between them and enemy states like Russia/China.

I think it's easier to turn the other cheek unless you really think you can suppress the enemy's response.