I think the issue with procedural loops (not to be critical, just in general) is that there's no abstraction - it's not clear what's getting mutated, or what the result is (or its type), it's harder to look at the individual steps, and it's harder to refactor.

The nice thing about functions like "map", "filter", "fold", "flatmap", etc., is that they describe intent - when you see a "map", you know it's not aggregating things, just applying a function: "map" has a distinct purpose from "fold" (and depending on how pure things are, you may not even be allowed to do anything crazy).

Aside from that, the higher-order functions have pretty intuitive algebraic laws for refactoring (like with "compose" mentioned in my other comment) - It's not clear how you'd factor code out of a nested loop without understanding the whole thing, whereas "flatmap" (a.k.a. "bind" for the list monad) has laws for refactoring it.