It's becoming more and more common for musicals to use songwriters from the world of popular music, with Waitress (Sara Bareilles), Kinky Boots (Cyndi Lauper), Ghost (Dave Stewart and Glen Ballard), Pretty Woman (Bryan Adams), The Time Traveller's Wife (Joss Stone and Dave Stewart) and one of the upcoming The Great Gatsbys (Florence Welch) being some examples in the last decade. By this I mean pop stars and producers writing original songs for a show as opposed to using existing hits in a jukebox show, as for instance On Your Feet, the Gloria Estefan bio-musical. did. (Hell's Kitchen, the Alicia Keys semi-autobiographical show uses a mix of existing songs and original songs all penned by Keys.)
Some of these shows are undeniably successful, both critically and commercially (eg Waitress) while others have met more limited success. What each of these shows do bring is the pop star's cachet which I guess is an important ingredient for marketing purposes. I suppose the thinking also goes that if someone can write pop songs that appeal to millions of people, they should be able to translate that skill to the musical theatre world. That clearly isn't always the case, otherwise The Capeman (music by Paul Simon) and The Last Ship (music and lyrics by Sting) would be huge hits.
I'm in two minds about this trend. On the one hand it (potentially) increases the crossover appeal of these shows. Theatre music used to be popular music back in the age of the Great American Songbook, but the two forms diverged in the 1960s, with only rare hits like Hamilton melding the two. On the other hand, I find that (with exceptions) songs written by pop music writers don't tend to be as good (ie suited to the dramaturgical needs of musical theatre) as wrongs written by writers who come from a musical theatre tradition. Or maybe it's just that my personal tastes have been shaped by "conventional" musicals (although that hasn't stopped me from enjoying shows that draw from more contemporary forms, like Hedwig and the Angry Inch).