If it weren't for Davis Bacon, people like King could have competed for jobs by being willing to accept a lower wage. If you've got a choice between inexpensive, inexperienced workers and expensive experts, it often makes sense to hire at least some of the new people. Their work isn't as valuable, but since their pay is lower, it may be a better deal for the money -- and if you hire a few old hands, too, the beginners can learn from them, making their labor more valuable to you and putting them in a position to charge more on their next job.
But if the law forces you to pay top-scale wages no matter whom you hire, there's no benefit to hiring the inexperienced people. For expert's pay, you can get expert's work, so that's what you do. The would-be beginner doesn't get a start. He's just not worth what you'd have to pay him.
Unions claim Davis Bacon is necessary "to make sure government buildings are well-built." Without first-class union labor, unions say, the buildings might not be safe. That might sound reasonable if you didn't stop to consider that most buildings are not government buildings, and they're safe.
There are some in Congress who realize this and want to repeal the Davis Bacon Act. There is almost no chance that they will succeed. The people who like the law make good money from it and lobby well. The people Davis Bacon hurts are less organized. When you're trying to learn a trade and become a productive citizen, you don't have much time to lobby your congressman.