Easy to explain.
The start up current for the compressor is very high and the working current is also not that small. Usually the engine battery is loaded directly from the alternator- so these current can be delivered directly on demand if not stored in the battery. Due to the short connection the voltage drop isn't that bad.
Supply batteries have:
a) a different discharge curve- long time discharge with low currents
b) they are not always charged, so the discharge can cause damages to the battery.
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C30 AMG 3.0L engine doing donuts
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