Where is this "$100k/person" statistic coming from? SF hates homeless people, so I kind of just don't believe that.

Your held hostage to rent where you live? Move.

That's great, I'm glad for you. Not everyone can do that. If 2/3 of your income is going to rent alone, where are you gonna get the money for moving costs? You're going to need storage and/or shipping if you're moving far enough that your rent is going to drop significantly, you'll also need first month's rent, last month's rent, deposit, setup fees for utilities, termination fees for old utilities, and maybe even termination fees for your existing contract which usually just means paying the rest of the rent for the term of your contract all at once. Then you need a new job, new community, new resources, new doctors, etc. And don't forget people who are unable to move to certain areas due to marginalization. Some areas are literally deadly to live in if you're queer or a person of color, and some areas are completely unlivable if you're disabled. What about people who are already homeless? They can't move because social services are tied to the city where they last had residence.

Earlier in the thread you asked "If it was somehow just as easy to build public housing, why wouldn’t they?". The answer to that is almost always "lobbying", or "anti-homeless sentiment". Why aren't they building public housing? Because people with beliefs like yours are pushing back against it. You're arguing that it doesn't work because it doesn't happen, and it doesn't happen because it doesn't work.