Why is an integer variable in PHP interpreted as a string literal when passed from Drupal to JavaScript via Drupal.settings?

...  
  Drupal.behaviors.designer = {
    // attach is a property of Drupal.behaviors.designer, that points to a method.
    // This method will later on get called by Drupal core on initialization.
    attach: function (context, settings) {
      // Here this doesn't make a lot of sense.
      // Here you are writing height as if it were the property of an object.
      // Technically it is not wrong syntax because everything in JavaScript is an
      // an object. That means methods are objects too! Which also means that your 
      // attach() method above supports both properties and methods.
      // However, here practically you are assigning the contents of settings.designer.jquery_modal_height
      // to the height property of the attach() method.
      height: settings.designer.jquery_modal_height,
    }
  };
...

So basically what you are saying above is

// Add the height property to the attach() method, and add some value to it.
Drupal.behaviors.designer.attach.height = settings.designer.jquery_modal_height;

I don't think you want to do that! Of all the Drupal JavaScript objects there are, I would not consider the attach() method the most durable object.

If you want to use the contents of settings.designer.jquery_modal_height, you either pass it to another method, or assign it to a more durable object. For example.

// Assuming you assigned the string "foo" to settings.designer.jquery_modal_height in PHP.

someFunction(param1, param2) {
  console.log(param1);
  console.log(param2);
}

var someRandomObject = {
  aProperty = "";

  someRandomMethod: function() {
    console.log(this.aProperty);
  }
}

Drupal.behaviors.designer = {
  myCustomMethod: function(param) {
    console.log(param);
  }

  attach: function (context, settings) {
    // Consume the contents of settings.designer.jquery_modal_height.
    // This should print your string properly.
    // prints "foo"
   console.log(settings.designer.jquery_modal_height);

    // Could print "foo". Maybe you should consider accessing myCustomMethod() through
    // the context variable passed into attach().
    console.log(Drupal.behaviors.designer.myCustomMethod( settings.designer.jquery_modal_height);

    // Probably won't work. "this" right now probably refers to "attach" and not "designer"
    console.log(this.myCustomMethod(settings.designer.jquery_modal_height));

    // Here we assign it to a local variable. Not a very durable storage location
    // because we are within a closure right now. As soon as the attach() method
    // finishes it's execution, localVar goes Ka-Poof!
    var localVar = settings.designer.jquery_modal_height;

    // But we can do some stuff with it in the meantime.
    // Should print "foo bar".
    someFunction(localVar, " bar");

    // Here we store our "Drupal setting" in a relatively more durable object.
    someRandomObject.aProperty = settings.designer.jquery_modal_height;

    // Should print "foo".
    someRandomObject.someRandomMethod().
  }
};

So the short answer is: you're probably doing it wrong, revise your code ;)