By maintaining a chokehold on who can supply a vital resource (labor) to businesses, Unions have a history of strangling their patrons - See Detroit. From a distributed systems perspective, Unions represent a single point of failure.
I'm entirely in favor of groups banding together to request, nee, demand, rights, pay increases, healthcare. Once they start having 'management' tiers of their own, they're no longer representing you - They're a corporation you work for, contracting to your nominal employer. Just being clearer about it doesn't work - Microsoft hires an army of 'contractors' who are abused in precisely the same way. Nor does having multiple competing pseudo-unions - There's dozens of headhunters to go through to work for microsoft, but they all compete on 'price' and drive wages down[2].
[1]http://www.nrtw.org/required-join-pay-teacher/ - "educators cannot be required to do more than pay a union fee (typically called an "agency fee") that equals their share of what the union can prove is its costs of collective bargaining, contract administration, and grievance adjustment" - Which is to say, you don't have to join the union, they just get to negotiate for you, take a cut of your pay, and be the intermediary that represents you - While you've proved your disloyalty to them by not choosing to 'join' them, so they have no actual incentive to do so. See also https://en.wikipedia.org/wiki/Friedrichs_v._California_Teach...
[2] The lightly fictionalized https://en.wikipedia.org/wiki/Microserfs, which still rings very true more than 20 years later.
Yes, a union is pretty much a corporation that supplies labor. The biggest difference is how they're governed. Nobody bats an eye if a supplier negotiates an exclusive contract.
Seniority rules are something unions negotiate for. Contracting firms stick warm bodies on projects all the time. That's between the supplier and the customer, not imposed by the federal government.
I agree it would be better to fix that, but as you said, it's a stretch. Good luck getting Republicans or Democrats to go for it.
They get around that by structuring all of the benefits in the employment contracts to cover only their members, and by negotiating exclusive employment contracts with employers (so that there are no non-members).
Put another way, 94% of people who are represented by an NLRB-governed union never had the opportunity to vote for or against union membership in the first place. Most of those are employed by employers with exclusive contracts ("closed shop"), and because the union itself is not required to stand for reelection (its representatives are, but the union basically guaranteed permanent representation[0]), it means that free-riders are a non-issue.
[0] The process of decertifying or deauthorizing a union is very strictly regulated and unions have very broad leeway in preventing it, so it almost never happens except in cases of criminal misconduct and the like.