> shape’s volume dwindles to zero, while its surface area grows infinitely large

I think it's easy to grok when you get it, but that's certainly counter-intuitive on the surface, no?

I won't say it isn't possible that someone might struggle with this—it's quite subjective, obviously—but I do think it's unlikely that anyone with a general understanding of both volume and surface area would struggle here.

Even just comparing two consecutive iterations, I feel confident that any child who has learned the basic concepts would be able to reliably tell you which has more enclosed volume or surface area.

I will happily concede that the part you quoted could be quite unintuitive without the context of the article or the animation included in it. :)