Keepatit, I think there's a general issue and a particular one. First, the general issue: it's often possible to complete a puzzle in which the clued answer is not the entry without solving all the clues. That was the case with the recent Listener 4392 (I had four unsolved clues at the end), and there have been many such Listeners in the past. In principle that is not unlike those cases where a solver enters the only answers that will fit the grid without understanding the clues.
In this particular case I had two clues to which I had no solution if I treated them as normal clues, but they were not supposed to be solved as normal clues. Admittedly, they were intended to trap solvers into treating them as normal clues, and they were very cleverly constructed for this purpose. I don't think it would have been possible to require solvers to show evidence that they had solved the clues in two different ways without a convoluted, possibly confusing preamble, and it would detract from the elegance of the puzzle.
Your proposal for the extra letters to be written below the grid wouldn't be possible either. Consider how solvers have found alternative parsings that generate different extra letters; in those cases the hidden messages force solvers to reconsider their choices. If the extra letters from rogue clues don't contribute to anything, alternative valid parsings could lead to an alternative sequence of letters, hence - horror of horrors - ambiguity.
I think you would be on stronger ground to criticise the fact that it's possible to complete the grid without really understanding the theme, as appeared to be the case from some earlier posts.