Creating a new page and automatically associating it with a template in WordPress

I found this question very interesting ,So here is what i have done to make this possible.

Fetch page template and add them as sub menu of Post type page.

function addTemplateAddNewSubMenu() {

    global $submenu;

    // here we are fetching all page template from current activated theme.
    $templates = wp_get_theme()->get_page_templates( 'page' );

    foreach ( $templates as $filename => $title ) {

        if ( $filename != 'default' && $filename != '' ) {

                // add page-template filename as query string to add new page link.
                $url="post-new.php?post_type=page&template=" . $filename;

                $submenu['edit.php?post_type=page'][] = array( 'Add new ' . $title , 'manage_options', $url );
        }
    }
}

add_action( 'admin_menu', 'addTemplateAddNewSubMenu' );

I have added page template as query string to

/wp-admin/post-new.php?post_type=page&template=template-contact.php

Making page template dropdown selected by jQuery and template Query string.

add_action( 'admin_head','selectPageTemplate' );

function selectPageTemplate() {

    global $pagenow;

    if ( $pagenow == 'post-new.php' ) {

        if ( get_post_type() == 'page' && isset($_GET['template']) ) {

            $template = $_GET['template']; ?>

            <script>
                jQuery(function($){
                    $('#page_template').val('<?php echo $template;?>');
                });
            </script>

            <?php
        }
    }

}