Save the_content into custom field

You can get the content with $_REQUEST, Try the below code:

add_action('publish_post', 'save_content_to_field');
function save_content_to_field($post_ID) {
    if(isset($_REQUEST['content'])) {
        update_post_meta($post_ID, 'desc', $_REQUEST['content']);
    }
}

UPDATED
With the below code if you want to sore with shortcode support:

add_action('publish_post', 'save_content_to_field');
function save_content_to_field($post_ID) {
    $post = get_post($post_ID);
    $result = apply_filters('the_content',$post->post_content);

    if($result) {
        update_post_meta($post_ID, 'desc', $result);
    }
}