Why can't I define an iterator on a string?

Question

Here's a contrived example.

I can do this with an instance an array:

function* cut () {
  for (let slice = 0; slice < 3; slice++) yield '';
}

const cake = [''];
cake[Symbol.iterator] = cut;
const slices = [...cake];
//=> ['', '', '']

But I cannot do the same with a string:

const cake = '';
cake[Symbol.iterator] = cut;
const slices = [...cake];
//=> ['']

Why?