Being able to make use of a computer to do basic statistical analysis which makes predictions about the real world is useful, whether or not you can compute the underlying integrals.

Maybe it is "useful", but it's quite literally Artificial Arithmetic. As I've been arguing, I don't consider "usefulness" in this sense to be a worthwhile purpose of education. As I said above, if a person really needs to learn this kind of ad-hoc skill, they can learn it when they actually need it.

On the other hand, I think we basically agree that Paul Graham's view of compulsory education as essentially a giant creche to keep kids busy while their parents go to work is roughly accurate, so this really is a discussion abot what colour we should paint the bikeshed.

Yes, that's probably right.