The Wizard of Oz was a fantasy and therefore something of a special case in the musicals' tradition. There was an unofficial rule that the public would simply not accept performers in films bursting into song or dance without any rational justification. But it had broken so often with impunity that, by the end of the 1930s, no-one believed in it any longer. Its legacy still presided in the colossal number of putting-on-a-show musicals. These were felt to take the sting out of the exotic and irrational side of the musical by placing the major numbers in a rehearsal room or on a stage (however inconceivable this might be in theatrical terms).
Even then, if the principals sometimes behaved a bit oddly by the standards of the day, well, show people were precisely that. This meant that in lieu of being smoothly integrated into the story part of the film, the numbers were isolated interludes which had little functional relationship with the rest of the film and were quite often directed by someone else anyway. Those who made costume operettas (like the Jeanette MacDonald and Nelson Eddy films) or out and out fantasies had more freedom in this respect, but few filmmakers had the special talents necessary to utilize it fully.