And after all that effort, an operator overload is still the "wrong" API for the job anyway, because: it's missing a crucial argument! Any binary (infix) operator can only relate two things, but typically when you want to print something you actually want to relate three things: the stream, the object or value to print, and the way you want values represented.

Oh, sure, you can manipulate this by inserting magic formatting objects, but that's not different from saying all functions take one argument a la Category Theory or Haskell without syntactic sugar. Or you could write a class or function that allows you to tag your object or value by changing its type to a different one so a different operator<< overload is called. In the iostreams design, you're only indirectly selecting which print function to use by manipulating either the stream or the printed object. But in actuality the types of your two arguments are not different, so either you must munge global settings on the stream or "hack" which operator<< overload is selected.

And that's the crux of the issue; what you "really want" is a stream API with three arguments: the stream, the object or value, and a pointer to a function (or function object) that takes the value and transforms it to a stream of characters. Why not just pass that function directly and explicitly? Of course that requires something that's not just a single chained infix operator; my thesis being that starting with that quirky choice leads to down a path that ends in a bad design.