We spend years learning "spelling", because the mathematical equivalent (arithmetic, up through calculus, linear algebra, differential equations, discrete math, etc) is incredibly valuable on its own—and that that value doesn't really require familiarity with the proof-based foundations underpinning it. Learning real analysis is valuable if you're going to be a mathematician, but as an engineer it won't help you get more out of calculus (at least, not compared to the cost of learning it).