I guess it's easier for me: the EE calls out the GEC system conductors.
As a general principle most AHJ are not going to allow downsizing bonding connections in the GEC System.
So if you have a Ufer using # 2 then that self same #2 is expected to be brought up to the GEC bonding/grounding rail in the Service.
Strictly speaking, a Ufer is a concrete encased electrode. Yet, it is commonplace for 'Ground Ring' sized conductors to be encased in concrete, too. Strict construction of the terms would require Ground Rings to be set bare into the soil, underneath the pour. I never see that.
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Out my way, #4 Ufers are explicitly mandated for 200 A Services. No ifs, ands or buts.
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Since one is expected to have an UNBROKEN CONDUCTOR RUN from the GEC up into the Service any effort to complicate it by downsizing with an irreverseable ( Cadweld/ultra-compression connector ) connector are entirely uneconomic.
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All of which makes me wonder why such brain matter is focused upon shaving that last itsy-bitsy bit of copper out of a job.
To my mind, the very short runs involved with GEC Systems make them no place to concentrate ones energies.
Instead, focus on clean, quick installations. That's where one makes it or breaks it.