Countries without a strong nuclear deterrence don't have a seat at the table in this new geopolitical era. Looking at you, Ukraine, Taiwan and (can't believe I'm saying this) Denmark.
France has a first-strike doctrine. It's unique in the world, and it scares the shit out of everybody. An EU arsenal would be a typical retaliatory-strike doctrine.
> How would nuclear deterrence work for small entities like Denmark or Taiwan against huge entities like US or China? it only works at similar sizes
It works as long as the harm that can be threatened is sufficient to outweigh any perceived gain of winning. Small states may not be able to sustain as large of an arsenal, but they also rarely offer as much value to a victor.
A nuclear deterrent is still a deterrent, no matter how small. No country (hopefully) wants to risk any kind of nuclear war. Ukraine would never have been invaded if it still had its nukes.
We cannot know. My best guess is that at some point in the future there will be a military conflict between two parties that have nukes. Pakistan vs India for instance. And although they have nukes they would fight conventionally unless one party is about to lose.