I'm curious about one point: it seems that programmed clocks (8051 based or not) use a single counter that is divided and the result converted to a HH:MM:SS format.

A "hardware" oriented isn't easier? I mean it:

a counter for seconds, that overflows and increment a minutes counter that overflows and increments a hour counter. each counter is stored in some memory position, these positions are then displayed...

At college during some point of my digital electronics course we had to implement a digital clock using EWB and we used that technique.

There is some reason not to use it instead the "big-counter" method?