Comment by jdhwosnhw

Sorry, yes, you did miss the point. Specifically for the case of estimating volume, you just need enough points interior to the hypersphere to get good sampling statistics (which would become a problem in and of itself, by the way, at sufficient dimensionality). But estimating volume (or pi) is normally just used as a pedagogical example of rejection sampling, it’s not (usually) what people actually use the technique for. Typically its used to draw samples from one distribution, X, that is notionally hard to draw from, by instead drawing from Y. The sphere case is just an example (its actually easy to draw from a hypersphere without rejection sampling) - but if you did try to use rejection sampling specifically, it would take you a long time and lots of compute resources to generate those samples (in high dimensions)