Huh? Currying doesn't require any nonlocal reasoning. It's just the convention of preferring functions of type a -> (b -> c) to functions of type (a, b) -> c. (Most programming languages use the latter.)
Of course it requires non-local reasoning. You either get a function back or a value back depending on if you've passed all the arguments. With normal function calling in C-family languages you know that a function body is called when you do `foo(1, 2, 3)` or you get a compilation error or something. In a currying language you just get a new function back.
Functions are just a different kind of value. Needing to know the type of the values you're using when you use them isn't "nonlocal reasoning".
And it's not like curried function application involves type-driven parsing or anything. (f x y) is just parsed and compiled as two function calls ((f x) y), regardless of the type of anything involved, just as (x * y * z) is parsed as ((x * y) * z) in mainstream languages. (Except for C, because C actually does have type-driven parsing for the asterisk.)
Another way to look at it: languages like Haskell only have functions with one argument, and function application is just written "f x" instead of "f(x)". Everything follows from there. Not a huge difference.
In an ML-like syntax where there aren’t any delimiters to surround function arguments, I agree it can get a little ambiguous because you need to know the full function signature to tell whether an application is partial.
But there are also languages like F# that tame this a bit with things like the forward application operator |> that, in my opinion, largely solve the readability problem.
And there are languages like Clojure that don’t curry functions by default and instead provide a partial application syntax that makes what’s happening a bit more obvious.
