The problem with gutting a score (as in "Sweeney Todd") is that it destroys the expectations of fans of the stage version. I believe that musicals translate best to screen when they use most or all of the songs, even if some of them are shortened, and even if scenes are moved around.
I may be in the minority, but I think that "Les Miz" and "The Phantom of the Opera" worked as screen musicals, despite the problems with some of the singing. The scores remained generally intact, but, in both cases, the writers and directors bowed to the differences between screen and film -- in each, they took advantage of the opportunity to cut back and forth quickly between scenes, to break up scenes that would have to run together on stage, and to add visual context. Perhaps most importantly, each took advantage of the absence of an intermission, by moving key scenes that ended Act I on stage; in my view, moving "Do You Hear the People Sing" and the chandelier crash improved both stories.
The only major cut that I can think of in POTO was the rehearsal scene, which I'm not sure would have worked on film. Conversely, in Les Miz, the addition of the song "Suddenly" answered a key question that the stage musical fails to address: Did JVJ view raising Cosette as merely the fulfillment of a promise to Fantine, or did he really love the child?
Perhaps with the trend towards releasing Blu-Rays/DVDs of Broadway shows, we can put the question to rest regarding whether movie musicals should stay true to their stage counterparts. If people can view the original stage production, they are not likely to feel cheated if the movie runs off in a different direction.
Audrey, the Phantom Phanatic, who nonetheless would rather be Jean Valjean, who knew how to make lemonade out of lemons.