You could hook into theme_{$post_type}_templates and add an identical “default” option at the end:
add_action('theme_page_templates', 'wpse_296283_theme_page_templates');
function wpse_296283_theme_page_templates($post_templates){
$post_templates['default'] = "Default Template";
return $post_templates;
}
Then you’d hide the first one with CSS:
add_action('admin_head' 'wpse_296283_admin_head');
function wpse_296283_admin_head(){
?>
<style>#page_template option:first-child {display: none;}</style>
<?php
}