Ooh, a prettier analogy than what I'd been thinking. (My first thought on reading that phrase was that {x∈ℜ|0<x<1} is also bounded-yet-infinite (though not of "infinite extent"). But the ... well, squiggliness and different-directions-ness and "ooh! makes pretty pictures" and being less convenient to sort into a linear order, all seem to make fractals much more suited to representing human diversity. So I like your conclusion better.)
I like that!