As has been pointed out many times on this site in various threads, income is not a measure of intelligence
It is, and vice versa. It's not a perfect measure, but if there's one thing that groups of people discussing political issues are bad at, it's dealing with coefficients of correlation that are neither zero nor one. Pick any measure of income you like. Pick any measure you like of educational outcome (as a proxy for whatever you want to define intelligence as). They're strongly correlated. It doesn't matter if you think that's nature or nurture, because the intergenerational effect means they go hand in hand. It's not a guarantee, and there will always be regression to the mean, but it is ludicrous to imply that, as a tendency, people who succeeded in education don't earn more than those that didn't, that people in high earning jobs are more likely to have succeeded in education, and that success in education is more likely to be associated with intelligence. You can drag out endless anecdotes to attack that: I refer you to my comment about people's ability to reason about coefficients of correlation that are neither zero nor one.
And what's more relevant here is educational outcome versus parental income. The US SAT is a good data set to look at, because it's taken by a lot of people, and the SAT Reasoning test (Critical Reading, Writing, Math) is taken (the same paper) by all candidates This graph is shocking.
It's as if you're saying that the educational achievement of any child who has parents that have a decent income doesn't matter and they shouldn't be provided with state funded help they need.
I am not saying that. I am saying that for a given level of innate ability (whatever that means) it is easier for a middle-class child to succeed than a child from a less privileged background. Same ability. Better outcomes. Everything from more help with reading at home to more money to go on University open days to more help finding work experience to more money to do DofE to piano lessons to having decent shoes to go to school in to having better advice on choosing GCSE options to more willingness to fund out of school activities to more access to their dad's mate who's a professor to...
If the children are struggling educationally with special needs, there is a parallel system of funding which is nothing to do with PP. Although, in passing, it's hardly I think contentious to point out that middle-class parents are also better at navigating the statementing system, more likely to be effective advocates and more likely to be able to afford the legal fees for an appeal to a tribunal. And I've seen the claim made that the middle classes are more likely to recognise problems in their children, seek out, and then obtain, statements, because they have a lower concern about being adjudged bad parents.
But PP isn't about that. It's about the observation that for a given level of ability, children from privileged backgrounds do better. If that's not true, why is Oxford 45.7% privately educated, while the University of Wolverhampton is 1.2% privately educated? PP is about trying to alter that.