Coloradan here who is having a home built currently, and oh yeah, I used to be a construction worker when I was in my early 20s:

The issue with the entire building industry is that they don't pay carpenters, electricians, etc enough. Period. They have been able to avoid paying enough by using what I refer to as "illegally imported labor" at below-market wages. (I like the term because the verbage puts responsibility on the hiring companies who are clearly exploiting un-documented workers)

Having worked in construction, I've seen what happened to the wages paid. Essentially the large home-building companies who build the bulk of homes in this country in single, large-scale subdivision builds have increasingly been able to lower the skill threshold for construction. This by itself would have lowered the barrier to entry for documented workers, and probably has a minor downward pressure on wages.

However, the lowering of the skill threshold also made hiring undocumented workers much more viable. I didn't have to speak Spanish to train guys to use a nail gun and a saw to do framing.
I usually worked on high-end, custom homes for the wealthy. These jobs paid well, required a lot of skill, and were pretty much exclusively staffed by legal workers. However, at times, I'd have to find work with the big builders doing the giant subdivisions.

They paid shit, and were largely staffed with undocumented workers. In North Carolina where I worked, the bulk of these folks came from central America. McDonald's wages were literally higher than what these folks were paid. McDonalds doesn't hire illegals, but construction companies do. So this creates a very weird situation: Why would an American work a dangerous, hot, back-breaking job for a lower wage than McDonalds?

The local construction companies in Colorado were decimated in 2009, and many never came back. Now, the bulk of building here is being executed by national builders who are used to paying low wages, and there aren't enough undocumented workers to fill the jobs at these artificially low rates. The worst part is that the low wages have caused documented workers to not even BEGIN to pursue construction, and therefore they aren't learning the skills (in certain markets), which creates a long-term labor supply issue.

There is a very easy solution to this:

Make all construction companies and their sub-contractors use E-verify. But that will never happen because congress has two parties who both have interests in not doing this:

The GOP loves cheap labor while simultaneously saying they want to crack down (using completely unrealistic plans by design) on illegal immigration to appeal to the bigots in their base as well as the "law and order" crowd.

The Democratic Party views illegals as a source of votes once their kids are old enough. They ignore the fact that illegal immigration helped to break the back of unions in the meatpacking and construction industries because they have long-since replaced alignment with labor with racial identity politics.

Because of this, I'm going to pay waaaay too much for my house, the workers will be paid too little, the house will take too long, will be built somewhat poorly, and the suits running the building company will make a ton.