I don't doubt that you've encountered plenty of homeless who are just drug addicted and not mentally ill. Apparently about 25% of them suffer from significant mental illness.
https://www.nationalhomeless.org/factsheets/Mental_Illness.pdf
So that's a significant portion, but it's not like the majority or anything. Plus, I am willing to bet the 75% that are not severely mentally ill are more likely to be approachable and easily engaged. They are also probably more likely to be asking people for money and not just wandering around shouting incoherently (I've seen that many times). I hate seeing people who are in desperate need, it can be genuinely upsetting. It can also be genuinely angering when people sabotage themselves and then force you into a position to feel empathy for them.
I'm not sure what to do about the homeless issues. If I had a great plan I'd write my congressman. Lol.