IMO as with all things money, it's all about negotiation. Of course a lot of negotiating power simply has to do with the market supply/demand, but a whole lot has to do with policy and rules. Giving more negotiating power to H1Bs would definitely put upwards pressure on salaries.
Re: construction workers. Same problem, worker's rights. A lot of construction workers are undocumented: an estimated 20 percent [2][3]. Undocumented immigrants have virtually no negotiating power. Allowing this solid 1/5th of the workforce to confront their employer without fear of deportation would go a long way increasing compensation for the industry as a whole.
[1]: https://nces.ed.gov/programs/digest/d22/tables/dt22_322.10.a...
[3]: https://limos.engin.umich.edu/deitabase/2024/05/28/undocumen...