The file descriptor (associated with STDERR) is variable

By similar logic, I can argue that "But what is used to inflate the tires of my car is variable: (insert demonstration of me filling my car's tires with tapioca)".

Where do you think Perl got the file descriptor that it associated with STDERR? It just grabs, hard-coded file descriptor 2. Why do you think the shell uses >&2 if you want to redirect to STDERR?

If you do something stupid and make it so file descriptor 2 is used for something different from STDERR, then you better not use system nor qx// nor anything that uses exec(3) nor anything that calls any external libraries. Because you've put your process into a broken state.

There are parts of Perl that write out errors through write_to_stderr() which knows how to write to tied file handles (see pp_warn in p5git://pp_sys.c. and warn_sv and write_to_stderr in p5git://util.c.). There are parts of Perl that aren't at such a high layer of abstraction and just write to whatever handle is returned by Perl_error_log. These write to the IO handle associated with STDERR if there is one, otherwise they fall back to the next level (see Perl_error_log in p5git://perl.h.).

There is a ton of Perl that is at this next (and lowest) layer of abstraction which just writes to file descriptor 2 (there are actually still a lot of layers of abstraction over the top of the hard-coded 2, but they don't have any practical impact as the end result is still just always using file descriptor 2).

(Update)

Yes, it isn't terribly difficult to use file descriptor 2 for something different from STDERR. Perl goes to some effort to keep fd 2 associated with STDERR, but you can still thwart those efforts. And there are even situations where that is a reasonable thing to do (which is part of why Perl doesn't completely prevent it).

But, yes, if you do such without knowing what you are doing, then you are likely to run into a few surprises.

If you just refrain from close()ing STDERR, then you will very likely avoid all of these problems.