I agree with most of your point but don’t quite agree the chance is zero, if you are at the top of the heap academically you do have a reasonable chance. Of course that’s a very tall order.
Luckily that is not something my younger kid cares about and my older one manage to get it so not my worry any more. But again it stands to reason that you ought to choose the high school for the experience your child will get while in high school, not as a very expensive ticket to top college. Because the latter is a huge gamble with massive potential for disappointment.