I should probably not have been sarcastic, especially when I agree completely about the importance of looking at math with a more constructive/computational point of view.

Now, I'm not a mathematician or a scientist of any kind, merely a dilettante textbook reader, but I'm not sure that approach is sufficient, or even most efficient to teach all subjects.

I think it arises naturally when you approach subjects where it's directly relevant: engineering, complexity theory, type theory, etc. and people who will need those insights will get them in due time.

But yeah, broadening the audience could help people get a better appreciation of the connections between pure and applied math.