To some extent, sure. But that's kind of one of the problems of a strongly class-based society. It doesn't mean the children are any less worthwhile or intelligent, it just means society needs to do more to give them opportunities, whatever that might be.
Agreed, and it's not even so much whether they value education, but how much they're able to share it with their children. It's a little better now due to the internet, but let's say when we were growing up and before.
Even if a family values education, they may not have had any to further their children's. Example: You barely have a high school education, your wife is a HS dropout. You want education for your children, but when your inquisitive child starts asking questions, you don't even know where to begin answering or even how to promote asking critical questions. You don't have the $3-5k for a computer or even a set of encyclopedias. That's a severe disadvantage compared to a kid who has parents with graduate degrees, access to the internet, books, travel, etc.