I like analog clocks as well (addition to digital).
Purely mechanical clocks are amazing for the ingenuity. That's where having grandfather clock would be nice.
Some analog clocks are electrical, but have an analog interface with a second, minute, and hour hand. Some are wall powered, battery powered, and I bet solar powered. Nuclear powered would be dangerous and overkill.
My two battery powered wall clocks sync themselves with NIST.
I have two clocks that don't synchronize with the atomic clocks. My CD/Radio/Clock in my bedroom. If it loses the power, its time needs to be reset. If my microwave loses power, it's time needs to be reset, but I don't bother.
I could count the clock on my oven. It is not analog, but then it is not really functionally digital either. The display only works if that part of the stove HEATS up. I don't bother with that either. Why set what I cannot see or use?
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Acronym Legend
OS = Older Son, YS = Younger Son
The most important two acronyms I know.