When I inspect service entrances in the Allegheny Power service area, I'll accept just about any depth that will cover the conductor & won't get washed away by the rain.
What most guys do is about 1 shovel in depth, about 6 inches.
It could be a judgement call about using #6, since it is only allowed where it is "free from exposure to physical damage." Whereas #4 can be used with no protection if it is not "exposed to severe physical damage."
I've seen some make an arguement for burial at 24" based on column 1 of Table 300.5 After all, this is a conductor, and it operates within the 0-600 volt parameters of the table. If I'm ever forced into burying the grounding electrode conductor that deep, I'll sub out that phase of the work, too much shovel time.
