This is the most important answer. Radiators are actually used in combination with heat pumps to cool up to a few degrees Celsius in a non-condensing mode.
The problem is, it isn’t really effective. To really cool down, the radiators would need to get properly cold, but that requires cold water leading to condensation everywhere. In the radiator, but also around the piping in wall cavities, where it will feed mold growth.
A/C’s don’t have this problem because the piping doesn’t get cold and the heat exchanger (inside fan unit) gets very cold and the condensate gets captured in a drip tray and pumped away.