Consider advanced component creation in virtual dom frameworks. Components may want to yield some render responsibilities to the end-user while not exposing their inner api. They can use currying here to hide details from the end-user while providing their own public api.
I've also seen it be useful when you have sub components editing different parts of a model. You write one generic prop-assigner setModelProp(prop, val) alongside the model in the scope that owns the model. Then you give each subcomponent a curried setter with the prop locked in. Those sub-components don't have the ability to edit the model any other way now, and you haven't written a ton of boilerplate setters.