for air conditioning and pressurization, Bleed air from various stages of the engine is taken via a FLOW CONTROL VALVE.
This hot air then split into two lines, one goes to the "Pack" for cooling
The other goes to the TRIM AIR VALVE ----> HOT AIR
Cooled air from the Packs are then connected to the MIXER UNIT to mix with the recirculated air from the cabin. ----> COOLER AIR
Now as for you question, why this can not be done by simply regulating the temperature by the packs is a very practically challenging one. As the cabin is divided into CKPT/FWD/AFT the temp needed in those zones could be varied!
And Pack is simply a machine that cools the hot bleed air down! but the temperature regulator system is the smart one to get the correct temp and supply to correct zone.
stand to be corrected though!