“Your example lacks relevance”
Ugh. It’s called reductio ad absurdum. You said “labor always produces value,” which is false. I proved it with an abnormal example. But it so happens to be not mine and an example with a famous pedigree. Keynes was reputed to have said stimulus spending would be worthwhile even if we paid men to dig up holes and fill them in. Or was it dig ditches? No matter.
Now, you may say no one is so foolish as to think doing so would produce value. But all sorts of tangible produce is valueless, as you must know. Like I said, you can redefine labor as fruitful labor, but that’s just as unrealistic as my example of fruitless laborious.
Labor for hire is assumed to have produced value, or the producer of said labor is terminated, except in government of course.
Your example simply failed, not necessarily in absurdity, but from shallow analysis. You cited an act that is common in commerce, but failed to see its common usefulness.