The workers don’t really have much say in how a pension fund allocates investments.

Vanguard, the company behind those funds exerted a lot of pressure on the industry by offering those for such low fees. There are still lots of other funds that charge high fees to this day though.

I am not sure about specific ETFs, but some of them will lend out their shares to make up for the no fees though.

Additionally from a cooperate governance point of view the ETFs will generally vote for whatever management recommends. If the majority shareholder of a company is an ETF then management doesn't have meaningful oversight.

If you don't want to follow a bunch of companies than Vanguard funds are probably a good choice though.

I think the argument is that even if this maximizes yield, on a market-wide basis it might be making workers worse off in aggregate because they make lower wages due to their money being spent to oppose worker protections etc., and that that harms more than a highest possible yield would help.

The issue is not finances, the issue is politics.