Alter a controller's render array via KernelEvents::VIEW

I'm trying to alter a contrib module controller's output via KernelEvents::VIEW. I want to display the output from the controller and append the markup returned from the event handler. This is the code I am using, but it doesn't work as expected.

class BuildAlter implements EventSubscriberInterface {

  public function alterBuild(ViewEvent $event) {
    $build = $event->getControllerResult();
    $build['content'] = [
      '#type' => 'markup',
      '#markup' => '<p>Added by ControllerAlterSubscriber.</p>'
    ];

    $event->setControllerResult($build);
  }

  public static function getSubscribedEvents() {
    return [
      // The VIEW event occurs when the return value of a controller
      // is not a Response instance.
      KernelEvents::VIEW => ['alterBuild', 50],
    ];
  }

}