Is there a $10 billion "fix everything easily" button you have in mind for homelessness?
The "fix everything" button is abolishing zoning laws, and its aggregate cost is negative. Aggregate cost is not the issue preventing problems from being solved.
how many homes can you buy for $10 billion? especially if you don't care too much about size, extra niceties, or location?
Homelessness and visible homelessness need to be distinguished here. The large majority of homeless people are not the ones you notice on the streets. Most try to be discreet. Some have jobs. A person who lives in their car is considered homeless.
The best measure to reduce homelessness is to provide timely support for people who are being evicted from their homes before they lose their jobs (which they might still have) and before their mental health deteriorates. This is the point at which assistance is most effective. You have heard the saying, "an ounce of prevention is worth a pound of cure". Such programs have been applied to great effect in e.g. London.
The way to respond to people who have experienced chronic homelessness with complications is different and more difficult.
$10 billion would build a lot of homes. If you give homeless people homes, they're not homeless anymore.
The problem is also political, unfortunately. $10 billion isn't going to change zoning laws and a NIMBY attitude of freezing things in time.
If they like that point in time so much, they should build a museum, sheesh!
You know oddly enough, if you just put someone up in a real place to live for like a year, that's enough for the majority of people to get back on their feet.