131027-1138 EDT
kwired:
Both my washing machine and dryer can be put into the on state with no power, and when power is applied they will start. If power fails they stop, and restart where they left off when power is reapplied. Mine do not have the new electronic junk. The word junk does not mean that electronic controls can not be made to be as or more reliable than the electro-mechanical units. My experience and many others is that some new stuff is not more reliable or effective.
I have continuously running pilot lights on my furnace and water heater. Virtually no problems over many years. Gas range top electric ignition does not work real well.
I have a GE wall oven that works fine except when turned off at its control panel it wants to randomly beep. Thus, the breaker switch is off virtually 100% of the time. I have a GE microwave that likes to turn itself back on after a timed function has completed, the door is opened, the contents removed, and the door reclosed. Nothing clears this except pulling the plug for a few seconds.
The washer and dryer are old Maytag, about 15 or more years old. Virtually no problems except belts once and a seal leak. Also the washer washes clothes, and has a better transmission than the new models.
And energy efficiency is of no importance if the machine does not reliably perform its intended function. Such as washing machines that don't wash, and toilets that require multiple flushing.
.