I am not an Epson tech (IANAET), so this is a bit speculative, but I had the impression that all recent Epson printers parked the head over the capping station when not printing in order to seal it and prevent it drying out. It's possible that older printers did not do this. The 2200 was a bit different.
The 3880 does a bit more, because if you don't print for several minutes (five? ten? never measured it), the printer goes into some sort of standby mode, and from what I can gather it also de-pressurizes the ink supply system, and to print again it has to re-presssurize it. At least that's what it seems like to me. Again, IANAET. I can't see that actually turning it off is going to do any more. The P800 surely behaves similarly?
If you're worried about power reliability you need a UPS and surge protection.