It doesn't dehumidify, which is important. In hot and humid weather, dehumidifying improves comfort. It also prevents mold.
So that's a real disadvantage compared to a normal AC, which does dehumidify.
However, you could combine them. Install a smaller AC system that uses less energy. It will probably still dehumidify enough. You'd still save a lot of energy this way.
A modern "variable speed" AC system should be a good match because radiative cooling doesn't work as well on cloudy days. A variable speed system can scale up (provide more cooling power and use more energy) on those days, and on other days when radiative cooling works well, it can scale down but still run a large percentage of the time to keep humidity under control.
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Above I assumed when you said "fresh air" that you mean air that is dry enough to be comfortable.
But you might have meant literal fresh air, i.e. outside air to replace inside air with chemicals, smells, etc. For that, there's heat recovery ventilation (https://en.wikipedia.org/wiki/Heat_recovery_ventilation). It can transfer heat and humidity from one stream of air to another. So you can pump your cool and dry but stale air outside, and bring in hot and humid by fresh air, but you can transfer the heat and humidity from the incoming air to the outgoing air as they pass each other.
So that's a real disadvantage compared to a normal AC, which does dehumidify.
However, you could combine them. Install a smaller AC system that uses less energy. It will probably still dehumidify enough. You'd still save a lot of energy this way.
A modern "variable speed" AC system should be a good match because radiative cooling doesn't work as well on cloudy days. A variable speed system can scale up (provide more cooling power and use more energy) on those days, and on other days when radiative cooling works well, it can scale down but still run a large percentage of the time to keep humidity under control.
=-----=
Above I assumed when you said "fresh air" that you mean air that is dry enough to be comfortable.
But you might have meant literal fresh air, i.e. outside air to replace inside air with chemicals, smells, etc. For that, there's heat recovery ventilation (https://en.wikipedia.org/wiki/Heat_recovery_ventilation). It can transfer heat and humidity from one stream of air to another. So you can pump your cool and dry but stale air outside, and bring in hot and humid by fresh air, but you can transfer the heat and humidity from the incoming air to the outgoing air as they pass each other.