The victims of the "bad" homeless are the rest of society. The victims are the people who are assaulted, they're the people whose property is damaged, they're the people who commute by car instead of by bus/train because public transportation isn't safe, they're the people whose communities are destroyed. The solution to this problem is to wall these people off from the rest of society.
The victims of the "good" homeless are the homeless people themselves. The solution to this problem is homeless shelters, universal healthcare, affordable housing, and a stronger social safety net.
The fact that we don't acknowledge how radically different these problems are means that we solve neither of them. Nobody wants to welcome the "bad" homeless back into our communities or give them free handouts, and nobody wants to criminalize health conditions that make it difficult to work, or temporary setbacks that could be overcome if they had a safe place to sleep.
The purpose the distinction serves is to have the correct conversation about these problems. It's to help the "good" homeless who just need a little help, and to limit the catastrophic damage the "bad" homeless are doing to our society.