If a device such as a DVD has a built in battery for back-up during power failures, then surely you are using extra lecky to keep it charged? A device without it would presumably use less? So turning it off is merely a way of expending extra to recharge it when mains returns?
I don't need a clock on a cooker to tell me when I might be hungry OR how long things should be cooked for. A good old fashioned clockwork watch is more reliable in many ways.
Like a clockwork alarm clock - the "Jock Clock Big Ben repeater" I still use when the need for earlier starts arise.