In theory, it should have been a pretty good exercise for the kids. Where the teacher screwed up was not following up with it as the author said. It could have been a great opportunity, but it seems to me the teacher blew that.

The author's objection in this case is that this was just another question on a worksheet that was graded right or wrong then the class moved on to other things without further analysis or explanation. Not that the problem was impossible.

If the lesson of an "impossible problem" was a deliberate assignment set with an educational intent then there should have been a follow-up or even a primer beforehand so that the "poor kids" are not left thinking that mathematics is just randomly weird and absurd.