I think those last 2 paragraphs are due to people approximating math that would otherwise be quite complex to calculate, or making models that are approximations due to widespread available technology. Just because I don't turn if I cross over Mt Everest, does not mean that is the fastest route by foot.

I'm not saying to not use these approximations.

I really recommend the book "Where Mathematics Comes From," to really think deeply about what math is to us as an animal. Even other animals can do some rudimentary math, and arguably athletes are doing math innately as they perform their sports. Birds and dolphins do physics and calculus. Sort of. In this view, what we teach as math to each other as humans is essentially a language describing these phenomenon and how they work together. Calling this approximation a "straight line" in this language sense isn't very accurate and it's what's causing the debate.