Why do turbo use engine intercooler?

This is actually related to the quality and temperature of the air. Because the temperature of the air after turbocharging will increase due to compression, this is a basic physical principle, and all kinds of air conditioners now use this principle.

The advantage of installing an intercooler is that you can open an air inlet in the engine compartment to divert the low-temperature air outside and hit the intercooler to cool down.