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.