I think you missed my point. I know this isn't how pi is calculated, that is completely irrelevant to what I've been trying to say. I also know Monte Carlo has other benefits, and that's entirely my point: the actual benefits aren't illustrated in the example.

what I'm saying is that the entire point of illustrating an algorithm by example is to illustrate the power of the algorithm compared to a naive approach, regardless of whether or not there is a better way to solve the example problem.

i.e., the example should motivate the algorithm. But computing pi is one of the worst possible illustrations of why anyone would use Monte Carlo, because it's inferior to the naive approach. i.e., it doesn't motivate why anyone would want to use Monte Carlo.