"Why the hell can't they do it based on their SATS? and reading/spelling age assesments?"
What makes you think that would be any better?
I don't know how the proportions compare to various 11+s, but I'm pretty sure SATs results are stratified according to parental income and class too. And if SATs become the basis for entry to grammar school, then everyone will just switch from tutoring for 11+ to tutoring for SATs.
And reading age assessments will always favour kids who have been brought up in literate homes, been read to and led to read themselves from a young age. You become good at something by doing it, and you start doing it by seeing those around you doing it.
I don't think there's any solution to the fact that children from homes that are (a) wealthier and/or (b) more supportive of an educational ethos, will make more progress academically. We can dance around in circles all we like changing the way we measure it, but it won't change the basic fact.
I can't help feeling a lot of people have got this issue the wrong way around. We focus on condemning parents who support their kids' education for getting some kind of "unfair" advantage, rather than addressing the reasons why some parents don't. Of which money is only one.