How to assign a custom post title to be the post ID?

You could set it to the post ID when the post is first created via the default_title filter.

function wpd_default_title_filter( $post_title, $post ) {
    if( 'your_post_type' == $post->post_type ) {
        return $post->ID;
    }
    return $post_title;
}
add_filter( 'default_title', 'wpd_default_title_filter', 20, 2 );