I agree with much of that, MaloC. By way of disclusure, my first degree was mathematics and my master's in Computing, so I am very much of the "sciences" nature.
At degree level, there is so much science and maths to learn that we generally are doing the same as at primary school but at a more advanced level. Learn this, become familiar with manipulating it, move on to the next thing. Deciding which of two experiments may arise at PhD level, but even there is is relatively rare and usually limited to justifying your thesis. It only becomes common when PhD people get into places like CERN.
In the same way it only really surfaced in my maths when deciding whether existing texhnique A, B or C is most applicable to this problem.

I completely agree that you should not be thinking of degrees as direct training. But that is exactly where the idea of scrapping degrees because they don't show "a good return on investment' fails. The relationship is far more subtle and indirect than that.