From a pedagogical point of view, I think it's a very strange choice to go with gradient descent in this case. It makes linear regression look like something much more complicated than it actually is. People might be misled into thinking they need to hand code gradient descent every time they do a regression, for their 100 point dataset.
I upvoted the replies about computational cost and stability, because they raise an important point. But what I was trying to talk about (as you are) was the presentation of the idea.
Linear models are much older than computers, dating back to Gauss at least, and they do not have anything to do with gradient descent.
