I think the main reason they don't give the results, is because it would generate huge aggro and criticism of their choices about who to take - and they want to remain independent and free to take whoever they please, without having to justify it to anyone.
If results were published, parents would complain if a lower scoring child got a place, but their didn't. It would also open the door to parents demanding to see the scripts and asking for re-marks and challenging the marking and offers. It would take up loads of time and energy for the school and challenge the flexibility they have to not just take exam results into account when deciding who to offer to. State Grammars have to purely allocate on exam performance - either purely by score for super selectives, or by a minimum score and geography too, or by a minimum score plus music or other aptitude. They cannot decide not to have someone because they didn't think their behaviour looked good at interview, or because their primary school reference revealed things the secondary wished to avoid. Independents want the greater info they can gather and to take it into account, but if results are released to parents, it muddies the water, becaue parents would only see the results aspect of the process and not the other aspects which they couldn't be party to, but fail to fully grasp that results alone were not the determinant of an offer.
Most schools say in their terms and conditions for applicants that results will not be released and scripts not made available. It is very clear.
Another good reason not to release results is that all pupils start the school on an equal footing - there is no sense for anyone of being the lowest scorer or the highest scorer, with the problems that would bring. It's why many state grammars only release actual scores to those who failed to get an offer, not to those who did.
Finally, independent secondaries often DO release results to Prep schools on the strict u distancing these aren't given to parents. This is to foster good relations with the the Preps and is a two way street. The secondaries want accurate references from the Preps and for the Preps to have a realistic understanding of the standard required so they can advise parents accurately about whether to apply or not - Preps want success, not failure. Seeing the results allows the Preps to recognise the standard required in different aspects, based on the results and their knowledge of the kids' ability. They can then more accurately advise parents toward the right level of school for their child, and also ensure they get a closer to 100% success rate. Sometimes Prep schools will also intervene over rejections and make a case for a borderline case - and secondary heads might well listen, as lomg as Prep Heads don't do it too much. The thing is, a Prep Head can do these things and use the data in a way a parent can't. A parent will always only be thinking of their individual child, but a Prep Head sees that child as part of a bigger picture of both the he lresent and future of many children, so that's why the information is given to them. There is recognsition of the Preps and Secondaries working together for each other's mutual benefit.
I think it's right that the results aren't released to parents.