That's not quite right, though - you only care about the average occupancy if your sorting algorithm is O(b) for b elements. If you're using a O(b^2) sort, you actually care about the root-mean-square occupancy (or in general just the average runtime, or just the total runtime since you'll multiply the average by the number of bins anyway).
The k-bin approach is definitely much faster than O(k log k), but I'm fairly sure it's slightly slower than truely linear, asymptotically, since the runtime will be something like 1+0+4+1 in typical cases, where linear would have to be 1+0+2+1.
Edit: on some cursory Monte Carlo testing, the sum of squares of occupancies actually seems to still converge on a constant factor (of two) times the sum of plain/linear occupancies, which I was not expecting but does make the above point rather moot. (Also, the sum of cubed occupancies seems to converge on a factor of five, which seems downright bizzare.)
(Tangential edit: The factors seem to be 1 2 5 15 52±2 200±20, which might be https://oeis.org/A000110, though none of the interpretations there seem obviously related.)