The engine anti ice system is designed to be ‘fail safe’ - in the event of an electrical failure the valves will run to ‘open’ to ensure engine anti ice is always available. To keep the valves shut requires power, which generates heat. This reduces component life. Most operators will leave the AI selected on when on the ground, turning it off after engine start if not required for takeoff. There is a slight benefit to starting engines with it on (less back pressure?).
The MEL allows an engine AI to be inoperative, as it will be in the ‘safe’ position should icing be encountered. There is a temperature and performance limitation but this is not of great concern in most operations.