I have thought about this too. My guess is that it has to do with rhythm just like you said. When i speak spontaneously i feel like i have no control over the speed of my speech, no matter how much i think about speaking slowly i just cannot do it. But when singing you have to use the correct sound at just the right time. Which makes you follow a rhythm. The same goes for saying the same thing in unison with somebody else. And to some degree i think you do this when acting or faking an accent too. I can also use this when reading out loud. When i read out loud i am completely fluent, I think this is because i form the sounds as if i was singing. And shutting my brain of and not really focus on what the words mean, only on how to say them.