You can specialise generic functions on built-in classes in standard CL. Lisp methods are specialisations of generic functions; they don't belong to a class in the way methods do in eg C++. The issue you're talking about is that not all functions are generic functions in Common Lisp, and you can't specialise ordinary functions.

There's nothing stopping you from doing

    (defmethod add ((x number) (y number)) (+ x y))
    (defmethod add ((x string) (y string)) (concatenate 'string x y))

or whatever (multiple dispatch, too), and you could even call it + instead of ADD if you wanted (but not COMMON-LISP:+, so other code would continue to work; your packages could import your + instead of the standard one).

"+" is a function, what makes it "right" to be a method?

You mean, what makes it right to be a generic function that has methods?

First, + does dynamic dispatch based on the types of its arguments. It does different things when adding fixnums, vs. integers, vs. rationals, and so on, as well as a default method that signals a type error (in safe code). So it has methods, even if they aren't necessarily implemented as standard methods (but they could be).

Secondly, a user might want to make + work on other, user-defined classes (for example, if he user wanted it to work on a class representing quaterions). To make that work, the user would have to be able to add methods for those classes. One can imagine many CL builtins being implemented as generic functions to which users could add methods. This would be consistent with the standard.

a function is just a method that returns a value. Why make a special case for it? Of course you can go the other direction and allow functions to return nothing (or a representation of nothing like nil). That's fine too.