Why don't they sing the extra verse that Sophie wrote for Way Back Into Love (the one about needing inspiration) at the concert at the end? Cora specifically asked for an extra verse because the song didn't work without it... well, clearly it did.
You mean in the show, at the end of the movie? I think they chose not to use the extra verse because it was written by Sophie when she was feeling sour and betrayed. It would kind of spoil the happy ending and the reunion of the two main characters putting the verse there and reminding the audience of an already solved conflict. Also they don't really show the entire song during the end sequence (perhaps precisely to not include the gloomy verse). Plus, if you search for the full version of the song around the web, Sophie's verse is actually included in it.