Employers absolutely do have more market power.

Imagine if most employees bring a contract of their choosing from one employer to the rest, and employers are the ones maybe hagling over specific provisions. Really imagine that. Totally different world right?

That's what it would be like if employees had more market power.

I agree - I was just pointing out the absurdity / inconsistency of the argument by AlexTWithBeard.

I don't think it is absurd or inconsistent. The UAW works very hard and effectively at ensuring that GM, Ford, and Chrysler hire as few non-union employees as possible. The UAW has monopolized the autoworkers labor market and thus have historically been able to extract great rents from it.

GM, Ford, and Chrysler on the other hand can do practically nothing to prevent a machinist or welder from leaving to work at literally thousands of other companies in dozens of industries across the country that require those skills.

The union doesn't bargain with the workers. It bargains with the company. All unions I'm aware of that have real power maintain that power by preventing their employer from hiring non-union workers.