When you think about why NATO was originally created and who has and hasn't joined since then, it's been about defending Europe from the Soviet Union/Russia - during the Cold War just Western Europe, later increasingly also Eastern Europe. It's fair enough for the US to be irritated about European countries that aren't doing their part in that, especially as the US wants to redirect more of its focus to Asia and defending its other allies there. But when you think about it, the 2 percent of GDP spending norm is a weird way of measuring that. In the end what's really needed is for Europe to be able to defend itself without needing the US, or needing the US only in extreme scenarios like if Russia would resort to nuclear weapons.
When I say it doesn't matter what anyone outside the US says, I mean that the US will make its own decisions, as it should, and it's not healthy for Europe to rely this much on the US and get so panicky when it looks like that support is going to be withdrawn.
I'm not sure what frustration and anger you're talking about... but since you're aware of America's nuclear sharing policy, you'll also understand why the idea of France and/or the UK sharing their nukes with other European countries doesn't seem particularly shocking or revolutionary. I think many Americans maybe don't realize to what extent the European Union is in fact a union and many people feel a connection to other member states that's not much weaker than the connection between, I don't know, New Yorkers and Californians. Though certainly that feeling of pan-European connection is much stronger among certain groups than others, varying wildly depending on age, education level, place of residence and other factors.
Japan seems like the most trustworthy new nuclear power for obvious reasons - though for those same reasons, its population might also be the most fervently against that idea. What's clear is that the world is becoming more multi-polar than it has been for a long time, or even ever before. And if only some of those powers or blocs have nuclear weapons, not even the most important ones but rather the ones that were either important in the past (i.e. Russia) or have always been small but managed to obtain nuclear weapon technology because they felt they needed it (Israel, North Korea, South Africa in the past, Iran's steps in that direction), that does seem like a problematic imbalance. Obviously I'd want that to be resolved by reducing the number of nuclear weapon owners, not increasing it, but I don't see any realistic non-violent path to getting all nukes out of the hands of Russia or North Korea (and as for Israel, only in the event of a true and lasting peaceful solution to their conflict, which to put it mildly isn't looking very close at hand at the moment).
My biggest concern with regards to nuclear proliferation is probably India and Pakistan though, more than Saudi Arabia and Iran, because Pakistan is an even more unstable country, the Modi government has its nasty Islamophobic side, they have a nasty shared history and even more ongoing disputes and conflicts that could flare up into a full-blown war.
