You keep going on about things not being mc/wealthy parents' "fault," Retropear.
These parents are responding perfectly naturally to the system they are presented with, where there is an arms race to get into a particular school. You can hardly blame them for doing so, any more than you'd blame someone for offloading shares when they think the price will fall.
The question isn't whether the mc parents are at fault, but whether we think an arms race system is necessary to achieve the final aim, which (I hope we agree) is high quality schooling to enable every citizen to fulfil their potential.
You've given a cogent example of the cost of this arms race, suggesting primary schools divert the pupil premium to tutoring Y6 pupils for an exam which exists only to administer the system, instead of using it on, say, involving parents through adult training courses (one highly successful project),
Some people feel an arms race is an inefficient use of resources and the results don't actually serve the children very well.
Other people love the arms race, because they believe it is skewed in their favour and will help them garner resources to their child over other children.
You can't blame them for wanting to seek advantage for their child. But it doesn't mean the state should enable this - and pay for it.