It is valid, it is just that the resulting definition of "interesting" is itself uninteresting. The value of a distinguishing function is its ability to split its inputs into various buckets. In this case the "interesting" is just the identity function again; you put in "the set of all numbers" and you get back out "the set of all numbers". While you can create super convoluted function descriptions that map to the identity function, they're really all the same.
To a first approximation, at least. As is always the case in math, you can always split finer, and the field of math readers of HN are most familiar with, computation, you can have visible differences in the performance of one identity function versus another. But broadly speaking from a "conventional" mathematical perspective, they're all the same and uninteresting.
If you also want to get all mathy, the argument does depend on the set of numbers being ordered. It breaks down on numbers that aren't, so, for instance, the proof nominally proves that all integers are interesting (since orders on those exist) but it is invalid on real numbers, complex numbers, and a lot of other things that lack orderings, because there is no first "uninteresting real number".
