In the UK, people who are annoyed by GA plane noise will look up the owner’s details (these are held in a mandatory, public database by the CAA, equivalent to the FAA) and contact them directly.
In Germany the aircraft registry is not public. But that's only a minor advantage. People who would need to look up my aircraft registration aren't usually interested when or where I'm flying. People who know me are interested. And they know anyway. Can't hide the license plate of my car from neighbors, can't hide the aircraft registration from family and friends.