Why do people sing in musicals?
People sing in musicals because their emotions are so built up that they just can't talk anymore. Think about it, have you ever been so excited that you couldn't express your feelings in normal words so you make a weird sound or weird body movement (just me? okay), musical improv is the same way. As actors (yes improvisers are actors) you have to convey your emotions through your expressions, voice, and your body. With musical improv, the song in the scene comes when your emotions get the best of you and you can't take it anymore, so you do what? That's right make up a song to express how your feeling.
I think with a lot of musical improv groups and musical improvisers in general, when we're first starting out we're supposed to sing about your want, and if you're mad, sing about why your mad, and there is usually little or no emotional connection behind it. When you connect an emotional need to your want in a scene, your song will be cued by your longing for something so intensly that you can't express it through dialogue, you have to express it through song.
This emotional heightening doesn't just apply to musical improv, it applies to traditional improv as well. You have to connect to whichever character you're playing in order for what you're doing on stage to be grounded in some reality. When I improvise, I like to play wacky characters, and for a while I didn't play them because of the notes I was getting which were "Your characters are not believable" or "You're being too wacky" when what I should have been told was ground your wacky characters in some sort of reality, and that reality can be an emotion. If you're playing a character that is 100% wacky off the bat, then how the hell is your audience going to root for them? How are they going to see themselves in that character? With emotions, everyone has emotions, and everyone at some point has been hurt, or been in love, or been mad, so play up those emotions in order to connect with your audience.
Emotions are a powerful thing and a lot of times they are not used in the improv that I've seen, when you use emotions, it ends up heightening your scene work and taking your improv to the next level.