Haha, good question as this stuff is literally my job! Few reasons:
- You may want to warm up the oil or cool it despite not wanting to send coolant to the radiator
- You may want to flow the cabin heater without sending coolant to the radiator
- Even if the engine is "overall cold", you have spots that get hot before others, eg: the head gets hot before the block.
Al that means a pump that keeps running, more of less depending on temperature, RPM, load, oil temp, cabin heating demand... couple with a thermostat is required.