MY electric bill dropped thirty dollars last month when I changed the heating elements and put a cover on my hot water heater. The lower element was burnt out so the upper had to work overtime, plus the loss of heat because of no cover. Live and learn.
I called the manufacturer of my water heater (bought in 1999) and they said not to cover it. Here, in Texas with our lime buildup, they only last about 8 years anyway. I do try to drain the lime off the bottom every so often.