The rubber seal at the bottom of the stat, the bulb end, seals outside leaks. The thermostat seal, the lip seal down in the housing, prevents leakage form the block loop to the cooling loop. If the seal wasn't there, there would be a slow steady overheat condition because the path of least resistance in the cooling system is back to the water pump inlet. The seal forces the coolant into the outlet of the engine and into the radiator. Coolant flow after the head gaskets is mostly flow, no pressure, other than the pressure the cap creates to raise to air to boil point. Without the stat or seal, the coolant will follow the suction back to the water pump.