Can an electrician install a smaller GEC than the plans show?

Not without written approval from the engineer of record. NEC 90.1(C) makes the code a minimum, so a design may legally specify more than Table 250.66 requires.

What is the largest GEC required to a ground rod?

NEC 250.66(A) states that where the sole connection is to a rod, pipe, or plate electrode, that portion of the conductor is not required to be larger than 6 AWG copper or 4 AWG aluminum.

What caps the GEC to a concrete encased electrode?

NEC 250.66(B) caps that portion at 4 AWG copper where the sole connection is to a concrete encased electrode.

Plans call for a bigger grounding electrode conductor than code. Can you downsize?

Not on your own. The NEC sets a floor, not a ceiling. A stamped drawing that specifies a larger grounding electrode conductor is a contract and design document, and the code has nothing to say about installing something better than the minimum. The person who can authorize the change is the engineer of record, and the AHJ approves the result.

Why the code cannot help you here

Section 90.1(C) of the 2023 NEC states that the code contains provisions considered necessary for safety, and that compliance with it and proper maintenance results in an installation essentially free from hazard but not necessarily efficient, convenient, or adequate for good service or future expansion. In other words, the NEC minimum is the safety floor. A designer routinely exceeds it for voltage drop, for future capacity, for lightning and surge performance, or because a specification standard the owner adopted requires it.

Section 90.4 gives the authority having jurisdiction the responsibility for making interpretations and for approving equipment and materials. The AHJ can accept an installation that meets code minimums, but the AHJ does not get to overrule the engineer's stamped design on a permitted project, and neither does the installer.

What the code minimum actually is

Section 250.66 and Table 250.66 size the grounding electrode conductor from the largest ungrounded service entrance conductor or the equivalent area for parallel conductors. Three limits in 250.66 cap it regardless of the table. Section 250.66(A) says where the sole connection is to a made electrode such as a rod, pipe, or plate, that portion of the conductor is not required to be larger than 6 AWG copper or 4 AWG aluminum. Section 250.66(B) says where the sole connection is to a concrete encased electrode, that portion is not required to be larger than 4 AWG copper. Section 250.66(C) says where the sole connection is to a ground ring, that portion is not required to be larger than the conductor used for the ground ring.

Those caps are why a 4/0 service can legally land on a 6 AWG at the ground rods. If the drawings show 2/0 to the rods, that is a design decision, and it is not wrong. It is just more than the code requires.

How to handle it in the field

Submit a request for information or a substitution request to the engineer, citing 250.66 and the applicable cap, and let the engineer issue a revision or a written approval. Get it in writing before you buy wire. If the engineer declines, install what is drawn. If the job is a design build with no stamped electrical drawings, then the code minimum plus whatever the AHJ requires is the standard, and you can size from Table 250.66 directly.

One more caution

Confirm what the conductor actually is before you call it oversized. Section 250.24(C) sizes the grounded conductor brought to the service, Section 250.102(C) sizes supply side bonding jumpers, and Section 250.122 sizes equipment grounding conductors. Those are different conductors with different rules, and a number that looks large for a GEC may be correct for one of the others.

Field takeaway

Build what is drawn or get the change in writing. Table 250.66 with the 250.66(A), (B), and (C) caps is the code minimum, and 90.1(C) makes clear that a design is free to exceed it.