If you look outside the US, you can get housing for a price that leaves enough of the 4000 for other expenses.
The easiest option is to connect some barren land to a city center with public transport in a climate zone that doesn't need much insulation. But that just as a proof of concept. More clever options can be realized.
I think you can work out the next flaw in the plan for yourself.
You call it flaw, I call it obstacle.
If you look outside the US, you can get housing for a price that leaves enough of the 4000 for other expenses.
The easiest option is to connect some barren land to a city center with public transport in a climate zone that doesn't need much insulation. But that just as a proof of concept. More clever options can be realized.