Granted most of my Haskell work is in boring line of business apps, so maybe partial application is more important in other fields.
For example, I very often write functions that take an initial parameter representing some sort of customisable context and then further parameters that are the right types to use with some standard higher order function like a map, filter or fold. Partial application then supplies the context and gives back something ready to pass into that HOF.
I just find the "plain_fn <$> weird_type <*> weird_type ..." e.t.c really convenient.
It's incredibly convenient to use, but sometimes when I look at 'idiomatic' React code, in particular in the context of Redux, I can't help but feel it's a bit too much, especially when I look at the code through 'teacher' eyes, and especially when it's combined with JSX. And that's not even mentioning the arrow function variants, default parameters, and other ESNext goodies.
And yet I find it difficult to keep my hands off it, because it's just so damn convenient.
"Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away. "
-- Antoine de Saint-Exupery
I actually think he has a point on those two in the context of Clojure specifically. The process of explicitly currying or composing functions (again, in Clojure specifically) is usually more verbose and IMO harder to read than just writing an anonymous function that expresses the same thing.