> and mostly irrational
I'd say it is quite rational. Real estate represents value, and value should be earning at all times. Owning it free and clear does not change that one iota. Rents are based on the value of the property, not the mortgage on it.
False, rents are based on what the market will bear. The value of the property is stickier than rents.
Plus one can be "losing money" on cashflow but earning money in equity, so one can rent for less than the mortgage while the value of the asset is rising even faster than the monthly loss. Of course this only happens based on speculation and having free cash to "lose" monthly.