Coolant needs some time through the radiator to actually cool and work. On hot day it restricts enough to let the radiator work. On cool days it lets you warm up quicker! No stat is just constant flow and no time to cool or warm!
This old wives' tale keeps resurfacing... generations of people apparently don't understand basic thermodynamics or physics. In a word, it is completely untrue.
The reason for a thermostat is to allow the engine to reach a MINIMUM operating temperature before the 'stat opens. Has absolutely nothing to do with "time in the radiator". If you leave out the thermostat, there is max coolant flow at all times, so the engine will take forever to warm up (and if it gets to 180 or your temp of choice, it means your radiator, fan or water pump is improperly sized for the ambient temp!)
