He’s mischaracterizing what the Davis-Bacon Act does. The Act, signed in 1931, requires that workers on federally funded or assisted construction jobs be paid at least the prevailing local wages and benefits for similar jobs in the area. Repealing it would result in reduced wages for construction workers on federal projects. This would lower the cost of public construction projects, as contractors could hire cheaper labor, but that likely would result in the hiring of less skilled and less experienced workers, potentially causing the quality of the projects to take a hit. This could result in higher long-term costs for repairs or safety issues.
This would also disadvantage unions. Unionized contractors, who typically pay higher wages and offer more benefits, could struggle to compete with non-union contractors willing to pay lower wages. This might reduce union membership and weaken organized labor in the construction industry.
Full contextual analysis of Section 3.9: Department of Labor and Related Agencies here.