However several people have done what you're suggesting by:
- Living on a boat (either out at sea, moored just off-shore, or at a marina). This can range from being cheaper, to being much more expensive.
- Campervan, or enclosed truck. They often park semi-legally overnight and move every few days to escape harassment. Bathrooms are problematic (gym? work?).
- Camping (i.e. just tent and woods). This often escapes harassment (since you aren't in a city) but you are limited by water, and often travelling to/from the site is time consuming if you wish to work.
- Living at work (if possible). Likely legal but can get you fired thus homeless.
- Living a hotel. Some people have claimed that they can live in a hotel for less than the cost of a mortgage + utilities + taxes + other expenses. Ditto with some cruises. YMMV.
- Living in a foreign country. If you work remotely living abroad or in the middle of nowhere can cost a LOT less than living in a big expensive city.
PS - In general being homeless is "illegal" in most US cities. You'd get harassed, maybe even arrested, just for being without a fixed address. Most cities will try to run you out of town (literally and figuratively).
RE: Shower/bathroom - PlanetFitness is popular amongst vagabonds from what I hear - $10/mo and has many national locations.
My neighborhood has had an increasing influx of these in the past few months. At first I figured, "Live and let live. If this is all they can afford until they get back on their feet, more power to them."
Since then, I've learned that the solution to the bathroom problem is often "shit in the alley behind my house", and their daytime activities typically consist of dealing and doing drugs and scattering trash. I ran out of sympathy right around the time I found a used needle near the front yard where my toddler likes to run around and play.
$7.74 per foot at the marina, and you get access to bathroom and showers. If you're willing to do some DIY, you can get a boat for a few grand. Plus, you get to sail around the bay!
Obviously not everyone is cut out for that, but it's worked for a Ph.D. I know.
You don't have to go abroad to solve that (unless you're from Singapore or something). Most (larger) countries have deprived areas where the local administration is perfectly happy to welcome anyone who works (in an "export" industry, selling something out of the area and this bringing in cash) and pays taxes.
And even combination of decent living and good telecom infrastructure is often possible.
I'm joking and serious at the same time: Living in a very constraint space is certainly not for everybody and - as far as I understand - highly taxing. I'm sure I could live in a sparsely decorated minimum sq hut - alone.
I have the world's best wife, but stuff us into a place like that and over time only one will come out alive..
A side effect of high land values is that the relative cost of teardowns/rebuilds is much lower, so you tend to see more replacement of the buildings themselves unless there are other regulations in place blocking that.