I agree with much of your post but let’s be clear, leading with this can be misleading.
Fundamentally, homelessness centers around being unable, for whatever reason, to work.
Not around specific wages and rents, which I think makes this part a red herring.
We can’t solve homelessness by attacking several ‘root causes’ at once. The key here is to be absolutely candid about what the root cause actually is right now.
Edit: Your comment is using homelessness to critique capitalism, and is not actually about homelessness at all.