A large portion of that spending is spent on prevention - getting rental assistance and other things to people who are in danger of losing their housing. There are over 400,000 "severely cost burdened" households that are "extremely low income" which is to say making less than 30% of median income which in LA means less than $20k/year, and spending more than half their income on rent.

You're looking at the most obvious symptom - people with no home - and saying "well if we just treated that symptom with all this money there would be no problem." But the root cause is an order of magnitude larger than that.