Transport aircraft and larger biz aircraft have airpacks handling the AC and at flight idle power settings there is less bleed air, and pressurization is a priority. The packs simply do not have full power when in a flight idle descent on many aircraft.
The aircraft I routinely fly have separate radial compressor driven refrigerant systems, and have large heat loads from onboard electronics and laser systems. They have to remain cool, and normally both AC systems are left on until just prior to engine shutoff after taxi. If it is a hot environment, we use the APU and keep the AC on after engine shutdown.
Once again, the situation is different in different aircraft, and is dependent upon the cooling system, the power plants, the installations and the design and operational goals.
Addendum #1: Some aircraft APUs can provide bleed air for cabin pressurization, but this is not universal. Also, some aircraft, such as the 787 do not use engine bleed air for pressurization, and rather use electrical compressors. The flow of pressurized air is rather constant in flight.