That's the nice theory, but in practice it's more like a prisoner's dilemma because they usually have more prospective employees lined up than you have prospective employers. They offer you a low-ball wage, either you take it and is employed and underpaid or some other guy takes it while you're still unemployed. If you'd all refuse they'd offer more, but as long as one of you is more desperate than the rest they continue their race to the bottom and they know in every pool there's someone who has hit that "Screw it, I need a job and I need it now" limit and will sign up. To a lesser degree everyone else who wants out of their old job too. Even if you think you're an above average negotiator for your profession - which you probably aren't - they've dragged the baseline down so low they can pretend to be generous.
Collective bargaining as you say won't be a perfect fit for the individual, but you're making the unsaid and wholly unsupported assumption that what's negotiable is a fixed pool which you get either way. "Give me X, or I walk out that door" is more often than not met with "Don't let the door hit your ass on the way out" while "Give us X, or we all walk out that door" is met with "Whoa whoa whoa let's not be hasty here, let's discuss this". If you get more power and can negotiate a bigger piece of the cake that way, then a slice of that can still be bigger than what you managed to negotiate on your own. They're just very good at making you think you did a great deal, that's what everybody's supposed to think. I think many would change opinion if they saw the salary pay-outs.