Please update the Page Template instructions

This page Page Templates gives a good explanation on how to create a new custom templates. HOWEVER, it fails to tell you that for a newly created template to appear the default page.php should also carry the following at the top of the page

<?php
/*
Template Name: New Page
*/
?>

There are a lot of people scratching their heads over this. Please make this clear in the instructions on the website and why not in the admin itself.
Thanks for the great work.