All coolant MUST flow through the radiator and any coolant that is not in the radiator when engine is off will be stuck in the channels of the motor, ofh, heater core and the expansion tank. Naturally during the transit process, the coolant will travel through many stops before reaching other stops... example, radiator flow to heater core then to ofh then to motor, then to turbos, then to waterpump then through thermostat and back to radiator. The trip is a one way trip and does not distribute itself from multiple places as you state: "thermostat can get its water from tank".... if it did that, the whole purpose of the thermostat to monitor and regulate motor, turbo heat would be defeated because the expansion tank is always cooler than the rest of the sections and therefore would give rise to errors in thermostat/motor regulation.
The expansion tank serves to give coolant if it is low, OR release overflow if it is present. It does nothing to regulate temperature relating to the thermostat. Also, the heater core is not a radiator, but rather it collects heat from the coolant to use if the driver wants to heat the interior... otherwise, it does very little to reduce heat from the coolant as it is hidden from air flow almost completely.
