While I think the west is a huge generalization, I don't think the west thinks children are capable of nothing. It's more about letting children be children and play. Rather than forcing them to "work" almost constantly from a very young age.

I don't really envy the school systems that force kids to work very hard from an early age to get into a fancy university. From what I understand it's usually school systems with a heavy focus on rote memorization as well and that takes up quite a bit of time with diminishing results.

Having been through a post-Soviet school system, it's not about rote memorization, at least not in maths. The point is spending as much time with a problem as necessarily, without having a predefined algorithm, until it cracks. It's such a useful skill and satisfying experience that I feel sad that some children are denied it for the sake of psychological comfort.