I'm surprised unions don't throw their weight around more via equity ownership in the company. Controlling the company directly is really the endgame move, once they control a majority stake, they're literally just negotiating with themselves for their labor contracts.
Even better, if they're managing their pensions via investment houses, why not just build their own investment house and leverage their negotiating position that way?
I'm surprised, I did a little digging and there are actually quite a few companies that are at least 50% employee owned[1]. The biggest company in the list is Publix Supermarkets, but there are also quite a few manufacturing and engineering firms.
Even better, if they're managing their pensions via investment houses, why not just build their own investment house and leverage their negotiating position that way?