I wonder how much empowered workers would bargain for wages vs other things they might want. For example, in the US, we public employees do bargain for higher wages, but we also go pretty hard for pensions, job security and lower health co-pays. Increasingly we are also bargaining for childcare help due to the insane increases in the cost of childcare (this is a genuine mystery to me: in the 80's early 90's my broke parents could easily afford to put me in full-time, quality childcare from like 3 months onward). In European countries with strong bargaining, workers demand more vacation time.

In short, I don't think it's right to imagine wages going up enormously with more bargaining power; I think it's more accurate to imagine benefits and terms of employment (job security, vacation, autonomy) going up. Not a normative point but more of a positive one.

I believe this happens because of how the union works. People who care a lot about some issue (e.g., parents caring about childcare) will push hard on the union to bargain for their particular benefit. Wage increases, by contrast, are spread over the whole union and thus expensive in total but not huge for any individual, so there is a sort of collective action inertia even within the union. A small wage increase would cost as much as a huge increase in childcare help, so the parents will be able to mobilize more easily. Personally, this arrangement me benefits me a lot as I care more about those benefits than salary.