In practice, American unions failed to see that. Even if we ignore the cases where leadership just enriched themselves, unions concerned themselves mostly with extracting as much value as the employer would bear, and to a lesser degree to shield employees from the consequences of their mistakes.
On the other hand, fluid capitals means jobs would have gotten outsourced regardless of union's stance. In Mexico, which is far from having the cheapest labor in the world, minimum wage is less than $5USD per day. There are loads of social problems derived from that, but the fact that this is feasible at all relies on a much lower cost of living compared with USA. Try to implement that on the other side of the border and you'd be facing bread riots in no time.
And, so what if the employees are trying to extract as much value as they can out of their employer? Isn't that what capitalism is all about? Isn't that what the employer is doing to the employees, and anyone else they deal with? Why do we see it as acceptable for the company to do so, but not the workers?
So toss out the idea of giving workers more leverage entirely, or try to adapt with the times? The relocation example shows that the business isn't on your side.
How many jobs has not having a union prevented from being outsourced? Even when not fully outsourced, how many of us work at companies that have foreign offices in certain regions that pay a fraction of the US going rate? Or that invest much heavier in lobbying for increased immigration than in worker training/re-training programs?