It’s really not a bad idea. Though writing a musical already functions a little bit like a writer’s room if you have a separate composer, lyricist, bookwriter, director, and producer.
IF they could fairly determine royalties/wages and crediting, having 4-5 people working on the book could solve some of the problems of representation and parity. One person is overseeing the overall writing (like the showrunner), but then you can have multiple perspectives to write for characters of different perspectives. Because each writer brings different strengths.
The key challenge is ownership. In TV/film, you’re writing for hire. In the theatre, the authors of the show own the copyright.
We’ve seen some bad flops with a committee of bookwriters (Gettin the Band was developed out of improv, Paradise Square had people being hired and fired constantly, etc) but it’s a system that COULD work if you set out with that model as the original intention.