Yes, while one could make the case that I should purchase and plug one more thing into my wall. Would it be impossible to place a small amount of memory on the board that remembers alarm settings? If this thing is built as a convenience, I don't want to have a bunch of other devices for convenience (a radio, a noise generator, an intercom....)

And it should be a wind-up mechanical one so that power failures don't affect it.

Mental failures affect those. I would never remember to wind it.