it's not just "and now, here's this song you remember, just the way you remember it", there are scenes where two or three originally-unrelated songs are woven together to reinforce or counterpoint each other.

Yes, that's always creatively interesting (I'm reminded of Voiceplay's arrangements again now).
Although of course it does -- like fan-fiction crossovers -- rely heavily on the audience being so familiar with the original as to appreciate what you've done, rather than simply taking it for granted that the number in question was always like that. (I'm not a fan of "Wicked", so I had no idea that Voiceplay's medley of that involved slipping lines from multiple songs in against each other until other people started raving about how clever it was.)