> just put the private fields in the parent closure where they can't be accessed externally

Your approach can't translate the following code:

    class MyNumber {
        #value;
        constructor(value) { this.#value = value; }
        add(other) { return new MyNumber(this.#value + other.#value); }
    }

The proper solution is to use a non-enumerable property with an unnamed Symbol name, which is possible but cumbersome.