Create service with argument
An entity handler class is instantiated via EntityHandlerInterface::createInstance static method, which takes the container as the first argument and the EntityTypeInterface as the second argument. 

So you would not need the service and have to use the injected container to instantiate your class.

class MyCommentStorage extends CommentStorage implements EntityHandlerInterface { 

  /**
   * {@inheritdoc}
   */
  public function __construct(EntityTypeInterface $entity_info, Connection $database, EntityManagerInterface $entity_manager, AccountInterface $current_user, CacheBackendInterface $cache, LanguageManagerInterface $language_manager) {
    parent::__construct($entity_info, $database, $entity_manager, $current_user, $cache, $language_manager);
  }

  static public function createInstance(ContainerInterface $container, EntityTypeInterface $entity_type) {
    return new static(
      $entity_type,
      $container-&gt;get('database'),
      // etc...
    );
  }

}