> Buildings are engineered to trap heat, so the heat doesn't dissipate at night and every day the indoor temperature rises, and rises

This makes insulation sound like a bad thing. The more insulation you have the less the indoor temperature is affected by the outside temperature.

> 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.

A common scenario is to have unshaded solid walls exposed to afternoon sun. Without insulation the inside of the house can be high all through the night. A good effect of insulation in summer is to prevent that effect. Important to note that it would be standard to allow cooling airflow in the morning.