In this scenario, there is no loss in competitiveness. The union bargains for pay when there is profit, and when there is no profit it bargains for capital. At the limit, when the workers own the company entirely, then their own self-interest will be to reduce their salary in order to protect their equity. In this sense, their salaries will fall in line with what they would earn in another company, or slightly higher, but they will have massively more assets and equity than if they didn't have a union.

Of course, in reality, if there was no growth there would be bigger problems, but you get the gist.

I really fail to see how unions in this scenario make the company less competitive, or create worse conditions for the workers than without the union.