Back in the good old days, there was an idle air control valve which would increase air flow to adjust the idle speed. Not any more. The computer reads the throttle position, speed of the vehicle, air density, air flow through the MAF, and a few other things.

When the IAC went away, the throttle body gets adjusted for the air flow rate depending on the throttle position. The computer knows what the idle speed should be and tries to compensate. But if the throttle plate is dirty and not closing corectly, your engine will get too much air and not enough gasoline and then stall.

No shop cleans the throttle, it is too labor intensive and no parts are sold to the customer. Regardless of the age of the AC compressor, the idle speed should remain constant. You might have a different problem, just that starting with clean components in the air flow eliminates the physical part.