that is basically a trickle-down assumption

Invoking Reaganomics is a red-herring. It's used as a response to the kinds/quality of buildings built in the short term (or currently are being built) as if that's the only kind that need to or will be built (however, it is the only kind that is and will be built without policy change and getting rid of NIMBYism). That's not the case. As I said, there needs to be a glut of all kinds of buildings being built. There is no reason to build anything other than high end currently, because availability is limited.

The reason I lean towards subsidized housing is because (yes, in the short term), it directly helps the people that are struggling, rather than relying on the playing out of complex economic theories

This is not an either or proposition, however it is often presented as one (and you just did with the use of "rather"). It is possible to subsidize those who need it in the short term and open up the market for a wider range of building with effects to occur in the medium and long term. Both should be done. Once the market forces take effect, the subsidizes won't be as necessary. Or alternatively, if you're completely right that the market won't fix any of this, the subsidizes will already be in effect and useful and they can continue and we'll have a larger set of housing stock.

Supply and demand is not a "complex" economic theory, and presenting it as complex is disingenous. What we have now, with perverse incentives, taking everything to the voters with propositions at election time, NIMBYism, subsidizies, uninutitive zoning, is what is complex and leads to unintended consequences. Make no mistake: we are where we are now specifically because of decisions made over the last twenty years (although, one can argue that where we are now is exactly where NIMBYs want us to be).

Directly building more residences is not the only thing that can be done to lessen this pressure either. There are huge swatches of the city that are undesirable specifically because of lack of accessiblity and transportation. Public works projects that directly benefit all economic classes need to be considered, and perhaps forced through.

However, none of these things can be done overnight and if we were to start today on any of them we wouldn't see any significant movement for a few years and the end result for perhaps a decade. That's part of the problem too: there's a desire to see the effects immediately, but there is literally nothing that can have effect immediately. But doing what we're doing now, restrictions on building, moritoriums for research (which is really just a delaying tactic—I don't believe any "impact study" in California is a sincere concern for whatever is being studied), isn't helping anyone and only serves to push prices higher in the shorter term.

Solely subsidizing housing doesn't address the fact that the spread between what lower income backets can pay and what is available is going to keep increasing, which is only going to serve to make subsidies more expensive over time. And continuing to increasingly pay more for something when there are other things to at least try to reduce the cost is a losing proposition.