Why using the children prop makes React.memo() not work

I've recently ran into a pitfall of [React.memo()][memo] that seems generally overlooked; skimming over the top results in Google just finds it mentioned in passing in a [React issue][regit], but not in the [FAQ] or API [overview][react-api], and not in the articles that set out to explain React.memo() (at least the ones I looked at). The issue is specifically that nesting children defeats memoization, unless the children are just plain text. To give a simplified code example:

const Memoized = React.memo(({ children }) => (<div>{children}</div>));
// Won't ever re-render
<Memoized>bar</Memoized>
// Will re-render every time; the memoization does nothing