Not quite, because you can have an open shop in a state that doesn't have a right-to-work law. Right to work laws only ensure that workers have the ability to dissociate from the union without losing their employment.

> Minority unions can bargain only for their members -- but as far as I can tell, members can't commit to be bound by the outcome, which undermines the union's bargaining power.

Alternative way of phrasing that: Only unions which represent the majority have the ability to compel all members to accept whatever terms they negotiate.

> Majority unions have to represent all workers in a bargaining unit

They have to represent them for things like grievances, yes, but that doesn't mean that they can't pick and choose which subgroups they advocate for in negotiations over others.

That's literally what negotiating is - you have to figure out what you're willing to give up in order to get what you value more. And a union with a heterogeneous membership will inevitably have to decide which group of members to prioritize over others.

The purpose of right-to-work laws is to limit their ability to marginalize minority members, because those minority members always have a second option that doesn't involve unemployment.