Custom frontend page for plugin without a ‘physical’ page?

“What I need is to have for example site.com/mypage/ but I do not want ‘mypage’ to exist in the backend.”

It’s a bit late, but maybe someone else is in a need for this as well:

Step 1
Create /templates/ folder inside your plugin, and create custom.php file inside of it, with temporary content for testing purposes such as

<?php 
echo "Hi";

Step 2
Add this code to your plugin:

add_filter( 'generate_rewrite_rules', function ( $wp_rewrite ){
    $wp_rewrite->rules = array_merge(
        ['mypage/?$' => 'index.php?custom=1'],
        $wp_rewrite->rules
    );
} );
add_filter( 'query_vars', function( $query_vars ){
    $query_vars[] = 'custom';
    return $query_vars;
} );
add_action( 'template_redirect', function(){
    $custom = intval( get_query_var( 'custom' ) );
    if ( $custom ) {
        include plugin_dir_path( __FILE__ ) . 'templates/custom.php';
        die;
    }
} );

Please note that plugin_dir_path( __FILE__ ) may not be appropriate function for your case, depending on where you will add this code.

Step 3
Go to WP admin -> Settings -> Permalinks and re-save them, to flush/recreate permalinks.

Step 4
Try to visit yoursite.com/mypage.
Clear your browser cache / history, or maybe even try incognito/different browser.

Step 5
Remove the testing code from custom.php file and add your own backend code.