If you're going to take the stance of (1) or (2) that serious drama should not have the actors and actresses breaking out in song, then the first thing you have to do is reconcile that belief with opera, which has lasted over four hundred years. Operas have presented significant plays, for example Otello, totally in song and have been accepted as jewels of culture, music written by many of history's most revered composers.
There are now so many genres of Broadway musicals that one can be forgiven, if not expected, to dislike some of them. It was the "book" musical that first raised musicals from popular entertainment to culture. The sources for the book were legitimate novels or plays. James Michener's Tales of the South Pacific won a Pulitzer Prize and Pygmalion was probably the most popular play of the best known English playwright of the first half of the 20th century. (South Pacific has now been joined by Hamilton as a Pulitzer winner.)
The next development from the book musical was a book based very loosely or not at all on an existing piece of literature. To me these are more spotty than those based on existing material, but a musical based loosely on Romeo and Juliet but mostly original could be the brilliant West Side Story.
But when you get to the current "jukebox" musical, although these may be highly entertaining, I don't consider them to be Broadway musicals. Aside from the certain-to-be weak book consisting of a shallow history of the musicians, the real failure is in the lack of an original score. The audience knows in advance the hits that it will hear.
Then we have the family musical, a new legit genre pioneered by Disney, of course, and the mystery musical, as in Phantom of the Opera and Wicked, which run forever but nobody knows why.