That's stretching the analogy too far, and adding biasing details to force the impression that unions are bad.
Here's another analogy:
Going to work without a union is like going to war without any military organization. If your enemy is well-organized, how smart is it for you and your fellow soldiers to attack individually in an uncoordinated way without any overall strategy?
That is perhaps a better analogy indeed, but still lacks a bit since each 'soldier' has different goals and capabilities, which may be curtained by if they organise. And the 'enemy' still requires you to cooperate with them at the end, to come to their side and help them achieve their goals, which again, would probably mean you would be fucked if you were fighting alongside, and midway decided that the 'enemy' was actually right and you wanted to work with them.
The other thing is that I see a lot of criticism of some practice or other of some particular union inflated into a critique of unionization in general. I object to that because 1) it often echos management's anti-union propaganda talking points, and 2) it denies the possibly to innovate in the area of worker organization. I think there's a lot of value for workers in worker organization, even for high performers, and I think that needs to be the focus.
Going to work without a union is like going to court without a lawyer. Are there incompetent lawyers? Does it cost money to hire a lawyer? Of course, but that doesn't mean it isn't a stupid idea to try to represent yourself pro se.
Unfortunately, workers in the US have been the subject to the equivalent of a fifty year propaganda campaign bankrolled by prosecutors (business owners) to convince people they're really better off if they represent themselves in court pro se (without a union). The sad thing is the campaign has worked surprisingly well.
Dropping the analogy, I think many tech workers are treated relatively well for now by employers. Sort of like a well-treated personal assistant to the boss, who is comfortable and has their small privileges compared to those in the factory floor, and therefore feels like they're more like a boss than a worker, even though that's not at all the case.
The startup ecosystem has also encouraged tech workers to think of themselves as future bosses rather than present-day workers, so they favor the policies they imagine their hypothetical future selves benefiting from, even though it hurts themselves and their friends today.