> This is done by choosing A and B such that the following integral is minimized

Which is an absolutely subjective choice in an of itself and immediately breaks the notion that curve-fitting done that way is going to be telling you some absolute truth about the function.

For example, you might want, at each point of the non-linear curve being fitted, throw a line perpendicular to its tangent, compute the distance to the linear fit, and sum those distances over all points of the non-linear curve.

About as intuitively correct (if not more) as the "fit" proposed, yet yields a very different result.

Statistics are by definition subjective unless you use a specifically demonstrated property of the particular way you decide to project your data to the simple-minded underlying statistical model.