

If you want all countries to give up their nukes then I would agree with that. Perhaps the US could theoretically achieve a world without nukes if they threatened sanctions against countries who keep nukes.
But in reality, if the UK gives up its nukes, no other country will do so. I think Europe should possess nukes for the foreseeable future. Like I said before, if Europe dismantles its nukes, all it would mean is that the US, China, and Russia would suddenly have a lot of leverage over Europe.
Russia and China are not going to give up nukes any time soon. If the US under a future president decided to try and negotiate disarmament to eliminate all nukes then that might work. I think that’s the only way Russia or China would give up nukes. Until then I think Europe should keep nukes as a deterrent.
So yes, multilateral disarmament could work, and could prevent lots more countries from building nukes. I don’t think unilateral disarmament is a good idea though.