Who still uses analog clocks though? If you don't care for modern tech, just wake up with the sun and you're on time anyway.
The idea of keeping track of this system in software sounds terrifying though. Getting rid of DST would simplify things, but this would ramp up the complexity a lot.
You can replace "analog clock" by "clock" in general. My computers update on their own, but none of my bedside clock, oven clock, HVAC clock, … do, and all of them are electronic.
Also many people do, in fact, enjoy wristwatches or analog wall-clocks.
The idea of keeping track of this system in software sounds terrifying though. Getting rid of DST would simplify things, but this would ramp up the complexity a lot.