If the government uses its own employees, they don’t have to worry about profit margins, and have greater control over material quality and costs (no cost+ on materials, either). I will also admit, though, that too few govt managers/supervisors are especially good at cost control, but this is usually at the top, not where union workers are involved.
What would happen if they accepted the lowest bid, and the contractor showed up with fresh (illegal?) immigrants with no experience, etc. and used sub-standard materials? How much would it cost to remedy problems that would not be as likely happen with union workers who are paid a living wage? As you know, with union workers, you know that you’re getting trained, experienced workers who can more easily be held accountable for the work they do.
Not saying there aren’t issues with unions and all the red tape, just saying that using the cheapest labor and materials won’t necessarily translate into savings over the long run.