Why is the compressed air (from engine compressors) taken from High Pressure (HP) stage instead of Low Pressure (LP) stage? An aircraft that uses Turbofan or Turboprop engines would be taking the compressed air from 3rd stage and 6th stage (varies) and supplying it to the Pressurisation and Air Conditioning Kit (PACK). This air is cooled, filtered, and then supplied to the Fdeck, FWD and AFT cargo zones for temperature control and breathing. If my understanding is correct, PACK is a kind of compressor itself which cools the bleed air for circulation purposes.

Because the engine has got LP and HP stages (i.e compressors), why can't the engine send the LP stage air into PACK just for filtering? Because LP air is surely cool air which I understand still requires filtering. Without knowing further , it surely saves a lot of effort for installing more compressors and therefore, creating a more complex pneumatic system. Has this not been done or is there something I am missing?

KR,
Coming from the compressor section of the engine, the bleed air is sent to the precooler. Even air from the "low" pressure section needs to be cooled before it is sent to the air conditioning system. Here is a precooler from a CitationJet:



The page with that image notes that the bleed air is "hot enough to melt insulation and alter the heat treatment on aluminum alloys." The precooler reduces the temperature of this air and regulates the pressure to the pack system.

When the engine is at low power settings, bleed air is taken from the high pressure section. The engine must run fast enough that this provides enough pressure for the bleed system to operate properly.

Once the engine gets to a higher power setting, the bleed air is taken from the low pressure section. At higher engine speeds, this air still has the pressure required to run the bleed system.

Since the bleed system needs a minimum pressure to operate, compressing the ambient air to this pressure will always add a certain amount of heat.

Here is a diagram of the bleed system, to help visualize what is going on. Note that even after the air goes through the precooler, it is still hot enough to be used for wing anti-ice.