Am I the only one here with access to the "American Electricians' Handbook?"
On the topic of ground rods, they have an interesting series of graphs. Before I discuss them, though, I want to bring up the mathematical concept of 'limits.'
A 'limit' is the value a curve approaches, but never quite reaches. For example, the series 1 + 1/2 + 1/4 + 1/8 .... on to infinity, approaches a total of 2, but never quite gets there. "2" would be the 'limit.'
Looking at the graphs relating to ground rods, two things jump out:
First, that making the rod longer results in little improvement after eight or ten feet. You're 'approaching the limit.' It's certainly clear that even an eight foot rod is NOT twice as good as a four foot rod.
Next, regarding a second rod .... the effectiveness of that second rod doesn't get much better beyond six ft. While having six ft. between rods is LOTS better than five ft., increasing the distance even further (say, to 7 ft.) results in little improvement. Six ft. is just about at the limit;' that is, performance is as good as it's going to get. Having the rods farther apart does no harm, but results in little improvement.
Looking at all this data in a 'big picture' sort of way, it's a bit easier to understand why the Ufer ground, the system of turning the entire foundation slab into a GEC, is such an effective method of grounding.
Regarding the comment made about 'there's a rod at the pole- why bother with the rod at the house:' You've revived some of the muddled thinking that led to Article 250 becoming such a witch's brew of conflicting concepts. While there will be SOME current flow between the rods, the dirt under our feet is not a very good conductor. That's why were use that nice, fat wire (the neutral) as our return path. It is the neutral back to the PoCo transformer that lets all the breakers and fuses work. The ground rod, because of the poor conductivity of the dirt between the rods at the pole and the house, is pretty much irrellevant in clearing faults.
The only electricity that benefits from having a good path into Mother Earth is electricity that comes from Mother Earth. This means lightning and static electricity- and not the stuff the PoCo sells us. Thus, there's value in every lightning 'target' having its' own ground rod.