The main reason people insulate an air conditioner's compressor is to reduce its noise. These devices, especially as they age, can become so noisy that people in nearby homes may complain.
An insulating blanket is the best insulation method for the compressor. The blanket is usually made of vinyl or ceramic fiber, ad the noise-absorbing material can reduce excessive sound greatly. The compressor is in no danger of overheating as a result of this type of insulation due to the refrigerant that is constantly in the device.
If the noise created by the compressor is truly excessive, the best option is to replace the compressor. Noise-reducing insulation may help for a while but probably not enough, and the noise will worsen as the compressor ages.