> The more insulation you have the less the indoor temperature is affected by the outside temperature.

Insulation isn't magic, over many days of hot weather eventually the building will reach equilibrium with the average outside temperature. This means it will be cooler indoors than outdoors during the day, and hotter indoors than outdoors at night.

However, the nights are specifically when you want a residential building to be cooler, assuming the inhabitants are not at home during the day. So the insulation actually makes the building hotter from the perspective of the inhabitants.