"Right to work" laws are also called "open shop" laws because that's what they mandate. Of course unions can choose not to collect agency fees in other states.
Going back to the beginning, you claimed that unions can negotiate closed shops. The Taft-Hartley Act outlawed closed shops, NLRB v. General Motors made union shops equivalent to agency shops, and 28 states forbid agency shops.
> Alternative way of phrasing that: Only unions which represent the majority have the ability to compel all members to accept whatever terms they negotiate.
No, those statements aren't equivalent. Plenty of other negotiations see parties authorize their representatives to agree to terms within certain parameters. Plenty of contracts commit the parties to accept the result of some process.
> 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.
They can't choose members as one of those groups. If other groupings correlate with membership, sure, they can get away with some favoritism. You originally claimed they can exclude non-members entirely.