With the system in recirc mode, it's just like a fridge EXCEPT that the fridge compressor is either full on or full off.
No. Cars are not like fridges. This was my point. My fridge runs for a few hours per day. It maintains its target temperature (5 degrees C) within roughly a degree. I tested a midsize car a/c system thoroughly once. With an outside temperature of 28 degrees, it managed to cool the interior to just 27 on average by running continuously. The thermal loss hugely exceeded the the capacity of the compressor to cool. The differences are that my fridge is not outside in direct sunlight, does not have windows and has effective thermal insulation.
A car's a/c system cannot chill its volume on a warm day in the way that a fridge does. Under these circumstances, the numbers on the car's temperature control dial much below ambient are pointless.
Yes, of course air hitting your skin will have a cooling effect
Despite the a/c being ineffective at reducing the temperature of the car's internal volume, in hot weather it is more pleasant to sit in the flow of chilled air than to be in its path and not have the compressor running. When the thermal losses are great, then being directly in the flow of chilled air becomes the benefit of having the a/c on.
Yes, of course air hitting your skin will have a cooling effect if you are perspiring...
With the possible exception of Prince Andrew, all people perspire when their core temperature is raised.
I don't know why you are trying to make up a new type of cooling.
Why do you say this? I am not.
Of course the internal temp is always affected by the outside temp in any HVAC system.
No it isn't always affected. If the thermal loss from the enclosed space is significantly less than the cooling power of the system, then the internal temperature is determined by the control system. In this case the system will operate like a well-well-functioning fridge.
Only if the loss is significant does external temperature have an effect on the internal temperature. For cars, the losses are massive and so they do not work like fridges, at least in warm weather. For buildings, there is a range of operation. Many buildings have large thermal losses and so relatively inadequate a/c power of course, but by no means all.