I think it's not a class issue or a money issue, but an issue of parents' own educational level/the educational level of their friends. That does correlate pretty well with class, but not perfectly.
If you and your friendship group all have degrees, maybe teaching qualifications or postgrad degrees, you can probably source teaching expertise across a fair range of subjects. So you won't be worrying hugely about that. You may well decide your child just needs to play out in the garden for the next three months. But you could get someone teaching them a broad range of things, if you chose to.
I know people whose children are being taught by people who are experts in the subject and have teaching quals. Those children are getting one-to-one support that's probably better than what's provided at school.
But plenty of people don't have that. My MIL is super keen on education. She could not be more insistent about how much it matters. However, her capacity to teach is minimal. She doesn't really know what to do, and some of what she would try is actually detrimental, because she doesn't understand what she's doing (eg., her spelling isn't perfect but she'll 'correct' her grandson when he's got it right).
It isn't her motivation that's lacking - it's her education. And the same goes for much of my DP's extended family. And they don't know the limits of their knowledge (because by definition, you can't know what you don't know). So you see people worrying horribly and saying 'I made Jack sit down all morning and do his sums, so he will keep up,' but you look at the page they've photographed from Jack's book, and you can immediately see he's not remotely understood how to do them and nor has his mother who 'marked' them.