Great question. We only really use dygn when we mean the explicit timespan, so it's generally not used in this sense even though it might have been a better fit otherwise. In extended senses, we do use dag in a more general meaning - e.g. det kommer att ta fyra dagar = it'll take four days.
But in any way, the names of the days and the words dag and dygn are all really, really old, so looking for reasons within contemporary language is likely to be pointless anyway here. :)