If it is the sole conductor to a ground rod, pipe or plate electrode, a #6 is all you need.
Concrete encased electrode only has to be a #4
All others are sized to table 250.66 such as the water pipe bond, building steel, and for parallel 500kcmil it is a 2/0 copper.
I don't know how any times I have seen electricians size a GEC to a rod from table 250.66
It seems around here not many understand the table and its notes, I saw a 800 amp service split to 4 200 amp main breaker panels,with a #4 from one panel to the water pipe, "well it only coming from a 200 amp panel" yes but see note 1. under the table:roll: