200amps service - ground rods instead of pipe connection
Your inspector is wrong. You can always use a larger ground.

NEC article 250.66 covers this in depth.

In fact, the code handbook (an expanded code book good with explanations of what the code is requiring) has a great exhibit 250.30 which shows connections to grounding electrode systems. 250.66.A states the connections to rod, pipe or plate electrodes is not required to be larger than #6 copper.

if your existing connection goes from the rod directly to the service panel only #6 copper is required. If the system connects to a concrete encased electrode from that point (point of connection to the concrete encased electrode) to the panel #4 copper is required to the panel, but #6 or larger from your ground rod to the panel or point of connection with a concrete encased electrode is all that is required.

I use #4 solid copper all the time as most new construction has a connection point with the foundation rebar, and then a second method (driven rod) is connected. Since I already am using #4, I run the couple of feet outside and connect the rod with a listed clamp, all on 1 piece of wire.

It is OK to go larger but not required.

This method is code-compliant for up to a 400 amp service.