There's a difference between "I don't want to join because I don't want to pay these dues (and I still get all the benefits)" and "I don't want to join because I disagree with them and they don't represent me, and I don't want them to purport to speak for me (and thus I also don't want to pay them to do so)".
The former is indeed a prisoner's dilemma. The latter is a valid complaint and an entirely valid thing to want. And the only answer I've ever seen given is "well then get involved and try to steer it in a direction you care about", with no allowance for people who don't agree with the direction it has taken and don't want to spend their whole career struggling (likely unsuccessfully) to change it.
I think collective bargaining is a powerful and useful tool, that in isolation, more people would likely support. I think it's unfortunate that that tool has lost a lot of its power, in part because it comes along with structures and assumptions that many people do not share.
As one of many examples: people often complain that a union shop values duration of tenure more than experience or skill, and devalues the latter because it's easy to objectively measure duration of tenure. I've seen people say "well, if you form a union, it doesn't have to work that way"; that's always spoken from the point of view of the people who put together or maintain the union. But that doesn't do any good if you weren't involved with the initial setup, and you're just faced with how it currently works. If you push for something else, you're tilting at a very large windmill. And it's valid for someone to say "I'd like to have collective bargaining, but if it's going to do something tenure-based then on balance I'd rather reject it".
The ability to individually choose to join or not isn't just a simple prisoner's dilemma where defecting is a loss; it's also something that gives actual teeth to a requirement to be representative of employees, if an employee believes they'd be better off with no representation other than themselves than they would with the current representation. That would have to be a pretty serious level of failure, if an employee believes that membership has negative value to them.
Conversely, it might also resolve the prisoner's dilemma problem if negotiated benefits were tied to union membership. While some negotiated benefits (e.g. working conditions) are inherently available to everyone, others (e.g. policies, vacation time, pay structure) may be such that they could be offered to those who are a member of the organization that bargained for them.