Rationale:

For historical reasons, the standard is correct as written. There is a subtle difference between the base class rdbuf() and derived class rdbuf(). The derived class rdbuf() always returns the original streambuf, whereas the base class rdbuf() will return the "current streambuf" if that has been changed by the variant you mention.

Permission is not required to add such an extension. See [member.functions].

In classic iostreams, base class ios had an rdbuf function that returned a pointer to the associated streambuf. Each derived class had its own rdbuf function that returned a pointer of a type reflecting the actual type derived from streambuf. Because in ARM C++, virtual function overrides had to have the same return type, rdbuf could not be virtual.

In standard iostreams, we retain the non-virtual rdbuf function design, and in addition have an overloaded rdbuf function that sets the buffer pointer. There is no need for the second function to be virtual nor to be implemented in derived classes.

Minor question: Was there a specific reason not to make the original rdbuf function virtual?

Major problem: Friendly compilers warn about functions in derived classes that hide base-class overloads. Any standard implementation of iostreams will result in such a warning on each of the iostream classes, because of the ill-considered decision to overload rdbuf only in a base class.

In addition, users of the second rdbuf function must use explicit qualification or a cast to call it from derived classes. An explicit qualification or cast to basic_ios would prevent access to any later overriding version if there was one.

What I'd like to do in an implementation is add a using- declaration for the second rdbuf function in each derived class. It would eliminate warnings about hiding functions, and would enable access without using explicit qualification. Such a change I don't think would change the behavior of any valid program, but would allow invalid programs to compile:

 filebuf mybuf;
 fstream f;
 f.rdbuf(mybuf); // should be an error, no visible rdbuf

I'd like to suggest this problem as a defect, with the proposed resolution to require the equivalent of a using-declaration for the rdbuf function that is not replaced in a later derived class. We could discuss whether replacing the function should be allowed.