Making it clear that I mean no personal offence to mr1hotrod, this whole discussion is absurd. While it is understandable that a person who seldom flies may find a routine go-around discomforting, talking about compensation etc is ludicrous. If we were talking about compensation if the pilot DID NOT go around, with whatever consequences that might have, it would make more sense for sure
Many unseasoned fliers, or even seasoned ones who have a fear of flying, worry about many events that happen while in flight. I've had people sitting near me getting worried with the noise of the gear coming up or going down, for example.