I have to say I do find the difference between maintained and independent sectors very striking in some respects.
For example, I went to two primary school Sports Days recently. The independent school (non-selective, indeed a large SN cohort) had the children running proper races and it was clear they had been taught a lot about proper athletics and had developed their running technique nicely, including the pubescent girls who traditionally avoid such activities, and the SN kids. I was pleased at how inclusive it was, despite looking like something out of a 1950s school story.
The maintained school Sports Day was somewhat anarchic, and the races were mainly of the obstacle race type, with children engaging haphazardly in random teamwork-based challenges, so of which were a bit silly (eg all standing still with bean bags on heads).
My question is what on earth is wrong with learning to run fast and throw things well? What they inadvertently ended up with at the maintained school was the naturally talented looking as athletically superior as ever, but the other children being deprived of the opportunity to really improve their skills. If the bar had been a little higher, and the necessary tuition provided, they may all just have pleasantly surprised themselves IMO.
For me this is something of a indicator for what's happening in the classroom. I think our education system is neither fish nor fowl at the moment. It produces largely self-orientated, individualistic workers, despite everyone's best efforts, yet the academic standards are a bit questionable some of the time (especially knowledge of the lingua franca and many aspects of numeracy).
This serves all our children poorly and the struggles of the highly intelligent are just one indicator of how the current system is badly adapted to the requirements of wider society. We have tried to tweak a Victorian model designed to train factory workers, instead of thinking the whole system through from the bottom up.