You’ve not understood.
Firstly the throttle body butterfly does not control idle the idle control valve does.
The next thing to remember is that if the aircon is switched on and you’re driving along then the idle does not need managing to stop the car stalling when you turn on the aircon.
So your concern here is that the aircon is not managing idle and this is causing your high fuel use problems which would only be an issue of your car was sat still with the engine running, in which case it’s probably the whole car running but not moving thing that is causing poor fuel economy.
In the past you’d turn on the aircon the engine would shudder then the idle would pick up. These days that doesn’t happen because they put components in the compressor pulley to take the shock out of the aircon being switched on, the have variable compression rate compressors which can start compressing gently then ramp up once up to speed and engines are much better managed where they don’t just rev the engine because the aircon is switched on they make tiny adjustments to the mixture to keep the car running smoothly.
Also aircon compressors are a bit more refined than they used to be and don’t require as much force and power to power them.
Non of this would have anything to do with the problems you’re reporting and if you where so concerned, try driving the car around with the air con switched off.
Honestly you seem to be grasping at straws but have not listened to a lot of the comments from other people who have asked for information or photos.
My opinion is the car is fine you just sit in traffic a lot with the engine running and so the fuel economy is poor, but you proved on a longer out of town run that everything was fine.
