I was listening to Empire State of Mind Part II and I couldn't help but feel that the original Empire State of Mind with the rap is far superior. Part II has the great chorus as does Part I but without the rap section the arc of the song feels a little weaker. Also, the radio version of the song California Girls does not have Snoop Dogg's rap section which I think really weakens the song. The song has a catchy chorus and a great melody but the rap adds a whole new texture to the song.
The song Airplanes and the extended Airplanes Part II has an incredibly catch chorus. Airplanes Part II only adds an additional rap component. Airplanes Part II adds a lot to that song even though the only addition is additional rap.
Why does rap add so much to a song? Most hit songs have a catchy chorus like the aformentioned Airplanes: "What if Airplanes in the night sky were like Shooting Stars...". You can't just repeat a catchy chorus and expect a hit song. What's done in Airplanes is that the rap section explains the chorus of the song. The rap brings more meaning to the song.
California Girls unlike Airplanes has a melody to go along with it's chorus. Somewhere in the midpoint there's the rap section but there's rap throughout the song. Rap just takes a song to the next level other than just being melody + chorus. Airplanes is a good song that can survive without a melody just do to the strength of it's rap.
The reason rap is so effective is that you can communicate a lot more than you can versus a melody where you have to worry about a lyrical structure. Rap also provides a contrast to the rest of the song that makes it more meaninful.
Can rap improve every song? Yes it can. How many great songs do we wish were longer? Rap adds that. Take a song like Billy Jean by Michael Jackson. Billy Jean is a brilliant song that falls apart in the end. The end consists of the chorus "Dance on the Floor in the round" being repeated over and over again until it fades out. If you added a rap section that gave more details about Billy Jean you would get a more meaningful song and you would get a better climax. You could have the rap go over the faded out chorus making that section of the song more interesting.
Every song, even classical music, should be altered to add rap to it.