How to optimize ‘select found_rows()’ query? Several ‘high load average’ alerts daily

Question

This should not break pagination:

add_filter('pre_get_posts', 'optimized_get_posts', 100);
function optimized_get_posts() {
    global $wp_query, $wpdb;
    $wp_query->query_vars['no_found_rows'] = 1;
    $wp_query->found_posts = $wpdb->get_var( "SELECT COUNT(*) FROM wp_posts WHERE 1=1 AND wp_posts.post_type="post" AND (wp_posts.post_status="publish" OR wp_posts.post_status="private")" );
    $wp_query->found_posts = apply_filters_ref_array( 'found_posts', array( $wp_query->found_posts, &$wp_query ) );
    if($wp_query->query_vars['posts_per_page'] <= 0) {
        $wp_query->max_num_pages = 0;
    } else {
        $wp_query->max_num_pages = ceil($wp_query->found_posts / $wp_query->query_vars['posts_per_page']);
    }
    return $wp_query;
}