I think there's a distinction here: Of course star players do not NECESSARILY make a team successful. I'm only talking about what fans want to see (like the movies: a bad movie with Marlon Brando is better than a better movie without him, as far as entertainment goes.). As kids, we also latch on to individual players (usually, although not always, stars--my fave was Jerry Casale!)
As for me 'trading my fandom' to LAD--in part, yes: I will watch LAD and SD games in preference to RS at times simply because I am familiar with the players (I admit I spend much of the winter in LA).