wp_get_object_terms count on taxonomies within an category archive

A simple function to count posts did the trick, but this is one more request in DB :

function count_posts_in_cat_by_custom_term( $category_ID, $custom_taxonomy_name, $custom_term_id ){
    $args = array(
        'post_type'     => 'post',
        'post_status'   => 'publish',
        'posts_per_page' => -1,
        'category' => $category_ID,
        'tax_query' => [
            [
                'taxonomy' => $custom_taxonomy_name,
                'fields'=>'term_id',
                'terms' => $custom_term_id,
            ]
        ]      
    );
    $posts = get_posts($args);
    return count( $posts );
}