Wrong date and time after battery died

Certainly looks like it, but you don't necessarily get a choice. All sorts of unplanned circumstances could mean you don't use or plug in your device for a while. The thing is - it happens.

If battery depletion is such a problem, ideally Apple would design in some protective measures to stop a totally dead battery occurring.

I'm pretty sure I shut down my machine before heading off on holiday and was greatly surprised to find it completely dead on return. None of my other machines (half a dozen devices from various manufacturers) had this problem.

Mind, I'm not going to dwell on battery management in this thread. It is about how you fix the date and time problem which occurs when the battery runs down. There are threads on Stackexchange and Reddit which detail a solution which works. Apparently these Apple forums and Apple support aren't aware of them, so I've provided a link.