I've never understood why people try to connect these issues. They're wholely unrelated. No one's like "oh, I can't find a house in my city, guess I'll just live on the street". In reality it is "oh, I can't find a house in the city. I'll move where it's reasonable". If I can afford a very reasonable rent, I can afford a ride out of town.
The homeless aren't homeless because housing is expensive where you are. There are places within reach where housing is cheap.