These devices were designed to be run 24x7, and their power usage is minuscule, personally I would just let um rip.
I am of the old school of thought that cutting the power and powering on silicon stresses it more than just letting it run. I don't know of any specific studies into this phenomenon, but I have seen a lot of anecdotal evidence that this may be true. I know 10 years ago you would have been told just to let it run. Now I'm not so sure.
Additionally you mentioned lightning, I also remember a time when the above advice was completely ignored during lightning storms, where I live we don't get many, but I would be lying if I told you I have never ran around the house in a storm hurriedly unplugging (not just turning off but getting at least a foot from the wall with the plug and device) all my computers and related equipment. It was a risk vs. reward thing, and the poor performance of the surge protectors of the day and the electrostatic sensitivity of the silicon of the day meant that leaving it plugged in was a bigger risk than stressing it by pulling the plug. Additionally if you lose power the plug will be pulled for you, further pushing the pull the plug theory.
Now I just leave it on due to habit and I don't stress during lightning (better protectors + better device design + cheaper devices = no stress). I love living in the future.