Nope, LA is too much part of the macro economy to make such an impact. Wood and labor doesn't have to come from LA and even if that would double (it won't) there would be a round zero impact on inflation in LA.
The land to be build was going to be sold anyways, you just get one bidder more, or several bidders less if the council makes requirements like x% social housing.
Please, forget anything you are worrying about here, it does not apply.
Literally every problem I mentioned is at its worst state possible. People with millions and billions simply waiting to buy materials or get land approvals. It’s a well know intractable problem [1] and really the crux of the problem.
If just these problems could be solved the state has more than enough funds to house everyone. What billionaires do would be wholly irrelevant (like it is now)
Please, forget anything you are worrying about here, it does not apply.