That has nothing to do with the C memory model, but how the CPU is structured. No modern CPU has an interface for bit-address accessing as far as I am aware...
C doesn't really know about bytes. It has chars, but I believe there are some constraints on char, specifically, they have to be big enough to hold the ASCII charset. (I'm pulling real deep here, someone correct me if I'm wrong)
If I remember correctly, it assumes the size of a char is greater than or equal to
seven bits, and a char is defined to be the smallest addressable unit.