If I'm understanding you correctly, when you say you do housing, you mean that you work on the construction side of things, either literally physically building homes or working with companies that do so.

How does this directly relate to, say, regulation on how many vacant homes a rental company can own? Or regulation on zoning / type of housing able to be built in certain areas?

"Housing not getting built" is not the only issue that needs to be addressed, and seeing as it's the only issue you've given any insight on, it's hard to believe that you, a single person in a country full of people trying to figure it out, "fully understand every aspect of why it's expensive." It doesn't matter to the average homebuyer how much a house costs to build, if the company that paid to have it built is selling it for 3x that price, or they're only renting, or they just want to let the house sit to drive supply lower.

There are reasons that houses are expensive to build, and there's reason that houses are expensive to buy. There's obviously a lot of overlap but they are not the same lists. There is regulation that exists that can mitigate the latter without exacerbating the former. You are simply refusing to look at examples.