One of the things about a lot of the great musicals is that they did the numbers in long shots, with relatively few takes. Fred Astaire always insisted on doing his numbers in as few shots as possible, so everyone would know he was really dancing instead of benefiting from editing trickery, and in long shots, so audiences could see his dancing feet at all times. The Arthur Freed Unit at MGM took this idea a step further by doing not only the musical numbers but the dialogue scenes in as few takes as possible; watch a classic Freed musical and you'll find very few close-ups, with camera movement often used as a substitute for cutting.
In Meet Me In St. Louis, directed by Vincente Minnelli (who always worked in long takes, no matter what the genre), the centrepiece of the "Skip to My Lou" number is a long, two-minute shot where the camera moves back and forth, up and down, from one character or group of dancers to another, not cutting until it's absolutely impossible not to. As described in this essay:
It starts when Esther enters the shot carrying a tray of drinks, and eventually ends much later when John sings "Lost My Partner, Skip to My Lou". This sequence is immensely complicated. The camera movements are all coordinated with the dance numbers in the film. The camera sometimes soars over the dancers' heads. It can move rapidly and forcefully, or make small adjustments. The most intricate dancing in the film takes place here, an ensemble piece that also contains many individual brief numbers for small groups of dancers. I cannot imagine how hard this was to rehearse.
You don't notice the lack of cuts, but you definitely do notice that the characters are really performing with each other instead of being pieced together in the cutting room. Of course, as noted above, a shot like this takes an immense amount of rehearsal for the actors and the camera (and remember that the early Technicolor cameras were very bulky and hard to move, which makes it all the more amazing the kind of elaborate tracking shots that the MGM directors were able to pull off). But it's worth it, and I think that something is lost when directors start cutting back and forth, MTV-style, as though they don't trust the performers.
Interestingly, a lot of movie musicals that have (in my opinion) too much cutting were directed by successful stage people. Bob Fosse, whose movie of Cabaret was the movie musical for people who didn't like movie musicals -- no unrealistic bursting into song! no plot numbers! -- often shows a number from different angles, as though afraid that we'll tire of his trademark shuffle if we look at it too long from one angle. Morton Da Costa, who directed an ideal cast in the movie version of his stage hit The Music Man, does a lot of standard angle/reverse-angle cutting, and won't move his camera unless he absolutely has to. Of course, some of the best movie-musical directors were also stage directors (Rouben Mamoulian, director of Love Me Tonight and Silk Stockings, also directed the original Broadway productions of Porgy and Bess, Oklahoma! and Carousel), so I don't want to generalize.