Should you run a car without a thermostat?

Lets clarify at least one thing about the opening and closing of a thermostat.
It does not jump fully open or closed at it's designated temperature like a valve. It sorta oozes open and closed.

And with no thermostat, the cool water coming back from the rad will have a better chance of getting pushed back to the radiator than the hot water at the back of the block.