A confusing case when using controller and controllerAs in a directive - angularjs

Question

If a directive is using a controller directly, why is calling a method on the controller by referring the controller by its alias, not doing anything?
Imagine we have the following piece of code:
var app = angular.module('App', []);
app.controller('MyController', ['$scope', function($scope) {
$scope.doAction = function() {
alert("controller action");
}
this.doAction2 = function() {
alert("controller action 2");
}
}]);
app.directive('myDirective', [function() {
return {
restrict: 'E',
scope: {},
controller: 'MyController',
controllerAs: 'myCtrl',
bindToController: true,
template: "<a href='#' ng-click='myCtrl.doAction()'>Click it!<a><br><a href='#' ng-click='myCtrl.doAction2()'>Click it #2!<a> " ,
link: function($scope, element, attrs, controller) {
console.log($scope);
}
}
}]);
While the first link won't work, the second will. To make the the first one work, I'd have to drop the alias, i.e. instead of calling the action by ng-click='myCtrl.doAction()' to call it as: ng-click='doAction()'
Shouldn't it work using the alias too? I mean, you are much more likely to find and reuse a controller, where the developers have attached actions to the $scope object and not to this

Answer 1

ControllerAs exposes the controller instance on the scope under $scope[alias].
In your example, the scope looks (conceptually) like this:
$scope = {
$id: 5,
myCtrl: {
doAction2: function(){...}
},
doAction: function(){...}
}
So, you can see why ng-click="myCtrl.doAction()" doesn't work.
The Controller-As approach has some benefits over directly exposing properties on the scope - one is that it does not pollute the scope (and its descendants) with properties that they may not need. It also inherently provides the dot-approach (.) to work properly with ng-model. You can find more information in this SO question/answer.