I think that one of the main reasons people love Sweet Chin Music so much is because of Shawn Michaels. That's only natural though. HBK is one of the best and most popular wrestlers of all time, so I think that people liking his finisher is to be expected.
Personally, I love Sweet Chin Music. I think its one of the best moves I've seen. While a large part of that is probably because Shawn Michaels is one of my favorite wrestlers, the move itself is also really cool. It has a tremendous sound, that massive crack you hear whenever it connects. It looks really real and explosive, and it often comes out of nowhere.
I do agree though that if it wasn't Shawn's signature move, people probably wouldn't like it as much. But I bet that if you ask people whose favorite wrestler is Stevie Richards, they would most likely say that their favorite move is the Stevie Kick, and not call it Sweet Chin Music.
Booker T used the same move in WWE, even though it wasn't his finisher.