Speaking as someone generally ignorant of unions, I believe the teeth of unions lie in the collective bargaining that comes from making them mandatory. With right-to-work laws in some states (and other countries) this is often not possible, so workers can choose to look out for their immediate interests which undermines the union's power that comes from representing most or all employees. In other words, unions generally require more than just freedom of association or speech.
> I believe the teeth of unions lie in the collective bargaining that comes from making them mandatory
I don't believe that at all, mandatory unions are illegal in Europe yet unions are stronger here. It wouldn't surprise me if making them mandatory actually makes them weaker since workers are so afraid of creating unions that could potentially harm them, while I can always ignore an optional union so they aren't a problem.
I didn't want to make a Europe-wide comparison as the roles of unions and the rates of union membership vary widely across the continent, including several places with lower membership than the US.
I don't think requiring unions is the only way to do it, but the countries that have a high rate of unionization seem to have other incentives in place, such as Sweden and Denmark where unemployment insurance is generally provided through unions in contrast with Norway or France, where this is not the case. The latter countries perhaps consequently have much lower rates of membership, closer to that of the US.