In order for for Joseph and Mary to travel from Nazareth to Bethlehem required a SUV. They at least had a donkey, camel etc. for the travel.
Those were not cheap. Joseph had more money than people let on.
You are right.
Homeless was probably not the right word. How about, “not connected” and thus having to get put up where you could. You’d still be in the shed behind the garage if you were in town for the superbowl and didn’t have a reservation.
If Joseph had more money than he let one, he was a cheap bastard, because he gave the peasant sacrifice (dove) at the ritual sacrifice of Christ’s birth.
(And no, I don’t think he was cheap.)