I believe you are wrong. 250.58 states what to do, not how to do it. No mention of size. Multiple rods make up a ground rod system, be it 2 rods or 10. Running the wire from rod to rod is the same as going to one rod, i.e. it's all the same system. Take this (imaginary) situation: a building has a nice new service fed by parallel 600s. It has building steel, concrete encased and ground rods as electrodes, and has a lightining system. By your rule I'd take a #6 to the rods then a 3/0 to the lightining system rod because I'm bonding the 2 systems together. What good would it do?
Point 2: One of the reasons that #6 is stipulated as minimum is because the code panels (long ago) determined that the earth could only absorb so much. That quantity of current could be carried on a #6 and transferred to earth on an 8' rod given a low enough resistance (25 ohm). Granted there are some arguments to change this but it hasn't yet happened.
