You’re right, but that is the motivation for the blog post. Learning is a form of fitting that performs better in practice than the curve fitting mentioned in the blog post when the required fit is nonlinear and/or high dimensional. The author is making the point that if the model is simple, since learning is just a form of fitting, why not directly apply standard curve fitting techniques?
In machine learning, a learned model should be able to generalize to unseen data. Curve fitting does not have that characteristic.
Curve fitting does generalise to unseen data, and can even do it well if the training data was representative of the test data.
I do not understand what you mean. The whole point of curve fitting is to evaluate your curve at points that were not seen.
as long as you're interpolating, it should do just fine.
if you're extrapolating, it'll depend on whether you've assumed the right boundary conditions, but that's true for any model
The difference between interpolation and extrapolation is not that relevant in dimensions higher than 1.