OK Dana but that is not the closed circuit in question. That is just a high gain error amplifier or ideal Op Amp. The answer to the initial question is simply. Vout = Vz The error amplifier nulls the output error with 0 differential input and when unity gain that error is neglible.
Yes that is the result when 100% feedback is applied, or very high levels,
like 10 to 100%. But if we fdbk .1%, .01% then the loop G drops like a
stone and all that benefit of internal G starts disappearing. Here is an
example of that applied to CM analysis :
The use of the "ideal" model is to replace the OpAmp in the circuit
with that model, then write the loop and node equations, and taking the
final equation when Aol approaches infinity, and as you say the errors
drop out. If we had set the external G real high with tiny fractional fdbk
to the OpAmp, then those errors become way more significant.
All this just a part of Classic OpAmp analysis.
Regards, Dana.