There were two types of film musicals: original musicals and stage adaptations.
Original musicals were dominant until the mid-1950s, and had some of the greatest songwriters in America contributing original works: the Gershwins, Porter, Kern, Mercer, Berlin, Fields, Rodgers & Hart, etc. These remain, IMHO, the greatest American musicals, from Love Me Tonight to Astaire & Rogers to Meet Me in St. Louis to The Bandwagon.
The problem now is that most original songwriting gets direct visual interpretation through music videos, so there’s no longer a need to compile them for a film (and let’s face it, most of those musicals were threadbare in plot and were primarily song showcases). The only films that really receive multiple original songs anymore are animated musicals, and even then that’s slowly being phased out (see the last several Disney endeavors, or any computer animated feature).
From the mid-1950s on, with the phenomenal success of Rodgers & Hammerstein, film adaptations became increasingly common, until, by 1960, the most successfilm musicals were translated from the stage. I find these films, with few exceptions (The Pajama Game, The Music Man, Cabaret), vastly inferior to the musicals from the previous decades. They also, I’d argue, contributed to the death of the film musical. Why? Because:
(1) The need to “open up” the musical by having real locations and protracted production numbers meant that they became more expensive to produce. Film is film so they couldn’t just shoot the stage musical; they had to make it bigger, longer, more colorful. This made them costlier and financially riskier.
(2) There was no need to nurture original songwriting talent for the movies if all you needed for a musical was to buy the rights and go pillaging on Broadway. Thus, when the larger, more elephantine adaptations became financial busts, there was no musical-writing tradition at any of the studios to provide an alternative.
(3) These adapted Broadway musicals no longer represented “popular music” the way the previous musicals did. Sure, original cast albums would peak at the charts, but the existence of the rock ‘n’ roll counter-culture meant that film musicals had a narrower, more limited appeal. Rock ‘n’ roll musicals existed (notably the Beatles’ efforts), but going into the 70s, the most successful were concert films or nostalgia movies (American Graffiti, Grease).
Ultimately, the film musical is dead because there’s no compelling desire for it. Decades ago, everyone knew the songs from South Pacific and there was an enormous market to gratify in a film version. Even earlier, radio stars were also film stars who you could build a film around. Tastes aren’t so uniform now, music videos (free on TV) more-than-satisfy those markets, and many of the essential conventions people were used to in musicals (breaking out into song, etc.) are not familiar to newer generations and thus are a harder sell.
The fact that the thoroughly mediocre, recycled Moulin Rouge could garner such praise shows how sad a state the genre is in. For my money, the musical Buffy episode was ten times more inventive, smarter, sexier, better-written, and more attuned to the musical tradition. That’s our current gold standard. Let’s hope more is on the way.