This is not it.

"or whether employers have a right to fire them (they mostly do)"

No - they do not. Employers cannot fire workers that are striking 'properly' (i.e. within labour code protections) - that is the very essence of the power of Unions.

Workers can walkout or 'strike' any time they want, as groups or individuals.

They can all quit, and even threaten to all quit.

They can even 'conspire' to all quit.

None of that is illegal - but the company cannot fire people if the strike is per regulations. They can fire them if the strike is not per regulations.

The notion of 'illegal strike' is misappropriated here.

The term 'illegal' or 'unlawful strike' really should be described as 'illegitimate strike', in which case the (non-market) rights that the government has afforded labour to 'not be fired' when they strike, do not apply.

Under specific conditions, the government protects workers who strike from being fired.

If those conditions are not met, then the protections offered workers are absolved, and so the workers can be fired.

Sometimes, workers will do a 'strike' together, without the backing of their leadership - this is called a 'wildcat strike' i.e. 'coordinated strike, technically not under the premise of the labour regulations'. This is an 'illegal strike'.

Someone 'walking out' and doing a '1 person strike' would be doing a mini 'wildcat strike' i.e. 'illegal'. They will be fired.

As you mentioned, the threat of a labour union just 'stopping production' would be scary, yes, but in most scenarios, the company - if they could - would definitely take the pain to get rid of the union. In a heartbeat. With joy and elation.

If you have antagonist staff that are threatening your operations by shutting down production, harassing replacement temporary workers, all sorts of tactics ... you definitely want that situation gone.

The owners would more than likely just let everyone go, and open the doors to hire new staff, and probably allowing regular workers to come back but not allowing the 'bad apples' (their purview).

In short: Unions derive their ultimate power form the ability to 'walk out' whilst at the same time being protected from being fired. That's the power that Union power rests on. Without that power, they'd be whittled away very quickly.

Danish white collar unions, a little bit like government unions, are very different from most of the traditional labour unions i.e. factory workers, auto workers.

In the later, unions can wield incredible power. At Beoing plant in Canada, 'Management' does not decide who does what job, or who gets promoted/advanced. Boeing basically allocates the # or roles and the skill sets. The Union leadership decide who gets to do what job, and it's almost entirely based on 'time in'. 'Seniority' is the golden power for union members and it outranks almost all other things. At a Ford plant in S. Ontario, the #1 job for the guy with the most seniority is to do nothing. Literally he sits all day in a room, overlooking the plant, watching everyone work. I think it's a historical artifact of when there was literal oversight needed, but obviously not anymore. He's like the King of the factory and rules all. He earns well over six figures to do that. Really nice guy though.