I’m not convinced that chain application and composition are meaningly distinct in anything but a syntactic sense if the language in question offers first-class functions and deterministic evaluation (eg no side effects). In mathematics, composition ($f \circ g$) is invariably described in terms of chaining f(g())—in fact, the composition operator is usually defined as alias for chaining. Yes, there are subtleties I’m glossing, but I don’t think support the thesis that function chaining and composition are significantly different at this level (i.e. the level of syntax and idiom rather than the level of Category Theory).
On the one hand, I do agree that in a language like Haskell it's almost entirely a syntax level distinction.
On the other hand, syntax level conveniences and inconveniences can have a big impact on how people use a language. (Eg in Haskell if-then-else is more hassle to type out than pattern matching. A slight nudge by the language design to make users prefer the latter.)
Once you have acquired the ability to see functions as objects in their own right, many more techniques become available. Think of eg parser combinators.
Technically you don't need the syntactic convenience to use parser combinators. But I am not sure they are worth the hassle without those conveniences. Eg Python has enough functional machinery to support parser combinators, but its options for defining functions (def and lambda) are just so cumbersome.
