These live broadcasts aren't meant to advance the careers of their stars. The star casting is meant only as a way to attract an audience. If Lady Gaga is a fan of Joseph, she'd do it because she's a fan. Carrie Underwood had no career reason to do The Sound of Music, None of the cast of the Wiz needed career reasons, Hairspray had the right caliber of talent, but wrong caliber of fame, but they didn't need it for career advancement. Same with Grease and the recent Jesus Christ Superstar. These stars did the broadcasts because they liked the material, and considered it to be a fun project to work on (and a challenge since it was live). Who knows why anyone did Peter Pan; they obviously couldn't get anyone with any real drawing power to do it, but Allison Williams described how much she loved the role and did it for that reason.
Ever since A Star is Born was released, people seem to be treating Lady Gaga as if she were some new discovery. She's not.