That being said, LA's homeless problem is largely due to the homeless rejecting housing, rehab, drug treatment, etc. In CA, a person cannot be committed to rehab or treatment against their will. This is the single largest factor behind why CA's homeless problem is so much worse than comparable locations.
Empathy won't solve anything until you convince the homeless "advocates" that rehab and housing is more important than the "freedom" of the homeless to do drugs and wreck their lives.
You are correct, though I'd shift the focus slightly to mental illness. Mentally ill homeless in LA are deemed competent to decide their own welfare, but not face criminal charges. Logically both or neither of those must be true. Leaving a giant gaping hole of "nothing can be done" in any long-term solution.
Something is really wrong with the world when a city throwing around billions of dollars for a sports competition thinks just moving homeless people out of the way is an ethical answer to the problem.
If there was anyone in the decision making process with empathy they might run "slightly overbudget" by a few hundred million to build a hospital, rehab center, and public housing development to get those homeless off the streets permanently.