Nothing is uncoachable, no, but if you give a child a few paragraphs and then ask some searching questions about what they've read - not bog standard verbal reasoning but some quite stretching, subtle ones - it's a damn sight harder to coach to that, than ut is a pair of sentences with similar but subtly differentiated vocab options, then telling them to use the correct choice, in a very time-pressured way. The latter doesn't test intelligence - the former arguably does. And the latter is a specific style of puzzle, while the former tests ability to think. You can still coach to it, sure, but you can also spend some time in most state schools in their G&T classes with the former without that totally wasting the time of the kids not applying to grammar, because what you'd be coaching would be critical thinking skills. Useful in any educational context. And exceptionally bright kids could make a good showing in that without any coaching at all - the puzzle-oriented/intensely time-pressured format, and they just can't. If I have time I might dig up examples of the two approaches, to show what I mean.
Obviously a more privileged start in life will often advantage a child at a level you can't ever begin to even out. But providing a system of exams that so blatantly advantages coaching, and doesn't even pretend to test innate ability is fairly whacked out when a major life chance is to be funded by the tax-payer. Another grammar school I know of became aware that the kids were comparing where they ranked in their intake cohort, and it was corrosive for yeargroup cohesion and morale, so they dug up data showing where past years were ranked when they left as opposed to arrived, and proved there was no link whatsoever. Which interested me, because why did nobody then start to wonder if that weren't prima facie evidence that their admission tests were unfit for purpose...? Seems it didn't. That would have been my first thought - it's not a subtle leap, is it?
The Sutton Trust is so concerned about the narrowing of class background for the intake of this school that they're funding efforts to widen it. That's a charity that usually focuses on widening admissions to top private schools. If state funded centres of excellence are increasingly the sole preserve of very privileged children, then there's a major problem.