Which is too bad, because a lot of these shows had real cinematic possibilities. Imagine an Oklahoma! movie that felt more like a movie Western, or a film of Carousel that had some of the spirit of Fritz Lang's non-musical version of the source material (which, happily, is included as a DVD extra), or a shorter, tougher, more war-movie-ish South Pacific. If The Sound of Music works better than most of the R&H movies -- I may not like what it's doing, but it certainly works -- it may be partly because the movie possibilities of the material were a little more exploited, with more ideas that were specific to moviemaking (and actually good ideas, not something stupid like those color filters in South Pacific). That might have had something to do with Roger Edens, the MGM Musicals veteran, who helped shape Ernest Lehman's script and came up, uncredited, with some of the most famous ideas in the movie, like the opening shot (this is according to the book The Fox That Got Away).
I also have a problem with some of the musical arrangements in these movies; Alfred Newman was a very talented arranger, conductor and composer, but he always made everything as big, loud and overblown as possible. (No man has ever loved wordless "aahhh" choruses as much as Newman did.) And Rodgers and Hammerstein's songs work better when given less syrupy arrangements; that's why the most musically satisfying of these movies is Oklahoma! because it used the original Broadway orchestrations (Robert Russell Bennett) and the conductor of the original Broadway production (Jay Blackton, who also created the famous vocal arrangement for the title song). A song like If I Loved You from Carousel -- the most ambitious and longest musical scene that Rodgers and Hammerstein ever undertook, and possibly the best scene in the history of Broadway musicals -- works a lot better with a less bombastic orchestra. You can get a sense of that in these mid-'50s clips from "The Ed Sullivan Show," which reunites the two stars of the original 1945 production, John Raitt and Jan Clayton.
Update: A commenter offers these corrections:
Robert Russell Bennett wrote the orchestrations for the film version of Oklahoma (and won an Oscar® for them), but they weren't the same as the original stage version. Unlike most movie-musical orchestrations, they are tasteful, restrained, colorful, and stylistically faithful to the original.
Per his autobiography, Bennett (not Blackton) is also responsible for the "second special chorus" vocal arrangement of the "Oklahoma" title song.