Does a matter whether a value is primitive or boxed

One can use typeof to determine whether a value is primitive or boxed.

Consider:

typeof "foo"; // "string"
typeof new String("foo"); // "object"

In combination with Object.prototype.toString we could define the following two functions

var toString = Object.prototype.toString;

var is_primitive_string = function(s) {
  return toString.call(s) === "[object String]" && typeof s === "string";
};

var is_boxed_string = function(s) {
  return toString.call(s) === "[object String]" && typeof s === "object";
};

Are there any use cases for these two functions? (Or similar functions for Number, Boolean, etc).

The concept behind this question came from the following Comment by T.J.Crowder.

Should we ever care whether a value we have is primitive or boxed?