The power thing is a red herring. "Analog" clocks are almost always electric and digital under the hood. And battery technology has been good enough for them to stay powered for longer than actual analog clocks for decades. If you really wanted to, you can create an entirely mechanical digital clock.

The main benefit of the analog style output is in the ability to quickly read the output. You can get an approximate sense of the time with a much quicker glance, even if determining the time to the minute takes longer than with a digital display.