The best plan here is to keep $800k in investments, move to rural nowhere and buy a huge house for $200k cash and live off the investment income entirely and not bother working. You can then rent off portions of the property (a bedroom, a basement, airbnb etc.) to surge your income if you need it.
If you don't have $1mil up front to start, like most people, building equity in the place you live makes far more financial sense over time than does renting because you both get to live there and because it doubles as an investment. Starting from the same lack of a million dollars, renting only covers cost of living and does not provide for any investment opportunity.
Your last point ignores the significant costs associated with 1. amortization and 2. the liquidity problem. First, given a neutral market, the house decays in value: appliances need fixing, floors, heaters, boilers etc. We are just used to rising prices due to speculation, but nothing guarantees the upward trend. Second, consider the cost of converting cash into house and the other way around: mortgage fees, interest, buying and selling fees, plus real estate taxes.
The New York Times has an excellent calculator on buying vs. renting. The math just does not support your conclusions. Buying wins out after 10-15 years GIVEN an upward real estate market. With any downturns, renting wins out indefinitely. Include the risk of investing into a single instrument (all you money is in the house) plus the stresses of ownership (shit goes wrong all the time and costs you money) and the picture is not so clear at all.
You are right that property ownership is more illiquid, but supposing I had a million dollars invested making me a better than 4.5% return, why would I pay rent when I could just buy a house with that money instead? At the end of the mortgage period I'd have my original investment plus ownership of real property, while the renter would only have their investment dollars and would have to continue the investment-for-housing scheme for the rest of their life.
> First, given a neutral market,
This is a false assumption as markets are almost never neutral. It's impossible to be a market oracle, but historic trends show a general upwards movement in most well functioning economies. It's a better than chance bet that most markets are thus net positive. You are correct though that nothing guarantees this upward trend.
The New York Times calculator is pretty good, but misses the simple fact that you need to live somewhere forever and not just for the period of a mortgage. Thus any comparison should be made with how long you expect to live.
The picture is very clear, you will likely need housing longer than 10-15 years, and if that's true, then buying property nearly always wins over renting.
Fortunately, at least for homes it's also a solved problem. Take your data to the below calculator, and get on with your life.
http://www.nytimes.com/interactive/2014/upshot/buy-rent-calc...
Think of the math this way. A $1mil condo in New York generates approximately 45k/yr income, or 4.5% return on investment per year in rents. Subtract taxes and amortization and ask yourself, can you get similar returns elsewhere? You could for example purchase an index fund with the same $1mil and contribute the gains towards rent. Either way you are living "for free."
It is however risky not to diversify. So if the $1mil is all you have and it is all in the house, you are in danger. Additionally, property is not very liquid. In the downturn it would be difficult to exit. For these reasons, I believe house ownership only makes sense as a portion of one's assets. Renting makes solid financial sense otherwise.
In the conversation of rent vs. own people often forget to take the opportunity costs into account.