Why can't you stringify a function expression?

JSON can't stringify functions at all, it handles them just like undefined or null values. You can check the exact algorithm at EcmaScript 5.1 §15.12.3, see also the description at MDN.

However you of course can stringify function expression by casting them to a string, try

console.log("" + function(){console.log('foobar');})

JSON has no means to represent a function. It is a data format designed for simplicity and compatibility across languages (and a function is the last thing that will be cross-language compatible).

From the docs for JSON.stringify:

If undefined, a function, or an XML value is encountered during conversion it is either omitted (when it is found in an object) or censored to null (when it is found in an array).

yourFunctionName.toString(); will also stringify a function