Compare that to pragmatism of not spending time trying to do what's not going to be needed.
You can always work around these issues after all the language is turing complete.
However, this is not about if there is a program that functionally equivalent, this is about writing code that is minimal and can be read well and can be supported easily over a longer period of time.
Beyond that, the author's proposed API is most definitely not the best API design to use here, even if the default parameters did work in curried functions. A builder pattern would make a lot more sense. Or just do as Cocoa already does and provide a request object that can be customized before initiating the HTTP call.
The worst code to support is "I don't use that but I might need it once."
His point is that this is not just a "perceived problem", but a real problem that affects regular working programmers. What's more meat-and-potatoes than HTTP requests?