All these songs contain vital information of one form or another that is gone if the song is taken out.
If you start removing songs from this movie the entire story falls apart.
Without the song, we don’t understand how they feel, and without that, their actions later in the movie would make no sense.
Take out “The Other Side” and Hugh Jackman’s P.T. Barnum and Zac Efron’s Philip Carlyle never become partners, because that entire transaction takes place in a song.