A couple of things: one, there is a selection bias involved, as another responder pointed out. You don't see the non-addicted, non-mentally ill homeless, or at least when you do you might not even realize they are homeless. Unless someone is pan handling, a homeless person doesn't wear a sign saying they are homeless. You probably walk by countless homeless people on the street that you don't realize you are homeless. Only the drug addicted/mentally ill ones look like the homeless you are thinking about.

Second, your observations won't tell you whether the drug addiction caused the homelessness or vice versa. Many homeless people turn to drugs to cope.

Third, you don't have to live on the streets to be homeless. Those people who are crashing at friends and living in unstable group housing situations are homeless.