You just said that AC can’t make an indoor space cooler than the temperature outside. This is completely wrong and easily disprovable by simply asking anyone who lives in a hot region. The air conditioned indoors is always MUCH cooler than temperature outside.
Like, how do you think freezers work? The temperature inside the freezer stays below freezing while the ambient room temperature is 80 F.
AC is an ACTIVE heat pump. It can push heat out to where it’s already hotter, because it’s using energy to do it. What you’re describing is a passive cooling system, but air conditioners are active systems that use energy to push heat against the gradient. It’s like how a passive water pipe can only have water flow down from it’s highest point, but a powered water pump can actively move water upward to a point above where it started.