While the primary purpose of the insulation is thermal (where I have no more expertise than the next person), I know that removing the insulation will make the garage noisier. The insulation absorbs sound energy from noise created in the garage (by car engines, door slams, human or canine conversation, exhaust fan). Without the insulation, such noise would be reflected by the hard surfaces and build up in the garage. For an example, clap your hands or talk under an insulated area of the ceiling and compare with how it sounds when you do it in an uninsulated area (e.g., just inside the garage door).
The most direct acoustical benefit of the insulation is to people trying to communicate inside the garage, not to first-floor residents.
Fortunately, some other materials that we may consider for replacing the existing insulation, such as some spray-on insulation materials, also have good acoustical absorption. It will be worth checking into this characteristic when deciding whether/with what to replace the insulation.
