This is part of what the labour movement in the States, in particular, often says is the potential benefit of a project labour agreement. They say, well, since our rates are the normal rates anyway, or whatever else, we'll give you a deal on our rates.
Actually, the labourers' union tried to get a project labour agreement with Windsor county back a few years for all the road work for the new bridge. They offered to give the county 50ยข an hour, which they could use for any fund they wanted or whatever else in return for getting a monopoly over all the work. The county turned them down.
Often a project labour agreement will be sold based on saying there will be a no-strike clause in the agreement, or they'll give you better overtime rates or something like that. But in the bigger perspective, whatever they give, they're taking away again.