Until you reach transient shelter beds, which may not be saturated in a region (in some places in Chicagoland the work is going into outreach to get people off the street and into shelter beds as much as it is in expanding the number of beds), every additional unit of housing you build frees up some unit at or below that unit on the stack of housing. The effect percolates all the way down to long-term supportive housing rooms.

I don't really understand the intuition people have for how anything else could be the case. You make new housing available, people move into it, leaving vacancies. Pretty simple.

0.2% of Americans are homeless.

Why is housing always about the homeless? Yes, getting people off the street is important. But there's few other topics where a solution that helps 99.8% of people is dismissed because it doesn't help 0.2% of people (I don't even agree that it doesn't help them, but I'll be charitable for the sake of making my point).

So you're telling me if an additional, say, 100k units came on the market in Denver in the next year, housing prices wouldn't fall dramatically such that all working people could afford housing?

Working people should be able to afford housing near where they work. So let's press the gas pedal on building. The mentally ill and drug addicted should be subject to mandatory treatment or jail until such time as their underlying condition is mitigated to the extent that they can work and afford housing. Free housing doesn't work. In fact, it exacerbates individual dysfunction. It is cruelty masquerading as kindness.

Lowering the rent stops people from becoming homeless which is a necessary element of ending homelessness.