As long as I've got That's Entertainment: Treasures from the Vault playing in the background...
Something occurred to me while watching the documentary about "The Masters Behind the Musicals." It's just a theory, but hear me out and see if it makes sense. (If the hearing and seeing doesn't make too much of a mixed metaphor, that is.)
The studios, and MGM in particular, all had pretty good machinery and staff in place in order to produce their films, from directors and producers to arrangers and vocal coaches. This came to a halt during the 1960s when independent filmmaking came to the fore.
Is it any wonder, then, that production of the Hollywood musical also came to a halt, as this particular genre of film was so highly dependent upon that support structure?
Yes, there have been musicals produced since the mid-60s, but they've ranged from the mega-productions such as My Fair Lady and The Sound of Music to more wildcat films like The Rocky Horror Picture Show, The First Nudie Musical, and Moulin Rouge! (the version with the exclamation point, not the earlier film with Jose Ferrer).
What I consider to be the Hollywood Musical simply cannot be produced today, because the means of producing those films is gone. It's not that popular music changed; Elvis had his share of films, remember, back when they were still being produced.
It's comparable to painters trying to replicate DaVinci's work, without knowing how to mix the paints that he used. It can be attempted (and I consider Chicago to be a very good attempt), but it's somehow not the same thing.