I think the show is pretty mediocre but I agree with the critics that said that this might be the best show that could have been made from this particular novel.
The novel is a cute read, I grew up reading about Meg, Jo, Beth, and Amy and loved them to death, but once I grew up I realized it really isn't a great piece of literature by any means. So yes, the musical is corny and generic, but I'm not sure anyone else could have made a really good musical from this piece unless they took major liberties.
"Some people can thrive and bloom living life in a living room, that's perfect for some people of one hundred and five. But I at least gotta try, when I think of all the sights that I gotta see, all the places I gotta play, all the things that I gotta be at"