I can't see how one could get through even basic algebra without developing this intuition, though o.o

And yet so many do. Numbers are horribly scarce in this area, though. Sometimes I get desperate.

Anecdotally, I do remember saying something very similar to high school peers, in a manner that assumed they already understood it, and seeing their face contort in exactly the same manner that it would have had I suddenly metamorphosed into a polar bear and started writing all the equations for fourier and laplace transforms using trails of volcanic ash in mid-air.

This was years after basic algebra had already been taught according to the curriculum, and we were now beginning pre-calculus (i.e. last year of secondary / high school here in québec, calculus itself is never touched in high school level courses).