Spivak's Calculus is intended for use in a two semester course covering differential and integral calculus. It is a challenging but rewarding introduction to calculus; in my opinion, this text is appropriate for math majors while other STEM students might be better off with a textbook that didn't focus quite so much on learning proofs. It was used at MIT for the first year of Calculus, but only by the math majors.
Michael Spivak is an American mathematician born in Queens, New York.
Yes, I'm not disagreeing with your main point. I just had first hand experience with Spivak.
Your point reminds me of an experience I had in grad school. A good friend in the program was from (communist) Romania. We were both looking at the weekly math challenge that one of our professors posted in the hallway. It was something like construct with compass and straightedge the eight circles that are tangent to all three given (arbitrary sized and positioned) circles.
I was good at geometry in school, very good, head and shoulders above my fellow students. I really had no idea how to solve the problem and was fumbling around with it when I Romanian friend took a look and knew the correct approach immediately. It involved an isomorphic mapping of the circles into some alternate collection of straight line segments, solving the problem in that space, and then inverting the isomorphism (I think. It was many years ago--before the fall of the Berlin Wall). His high school training in geometry was clearly much deeper than mine was.
Read about Spivak's Calculus.