The cervical and lumbar enlargements exist on the spinal cord as a result of the increased nerve input/output required for the arms and legs respectively.
However, I don't understand how the enlargements could exist by themselves without the rest of the spinal cord getting thicker.
The following is an exaggerated view of what I think a spinal cord should look like. The cervical region needs to be thicker as it has to accommodate the original nerves from the legs (blue) AND the new nerves from the arm (red). There are now ~2x as many nerves needed to go to the brain - thus the spinal cord above the cervical area should be twice as big. It is not - it just enlarges around the cervical area and returns to normal.
Why does the spinal cord not get thicker the further up we go? Doesn't it need to accommodate more nerve fibers and thus be thicker?