cameronjonesweb-delete-default-options.php

<?php
/**
 * Delete the option setting for the default category
 *
 * @link https://cameronjonesweb.com.au/blog/how-to-remove-the-uncategorised-category-from-wordpress-and-woocommerce
 */
function cameronjonesweb_delete_default_category_option() {
	if ( get_option( 'default_category' ) ) {
		delete_option( 'default_category' );
	}
}

add_action( 'init', 'cameronjonesweb_delete_default_category_option' );

cameronjonesweb-filter-taxonomy-args.php

<?php
/**
 * Remove default terms from categories
 *
 * @link https://cameronjonesweb.com.au/blog/how-to-remove-the-uncategorised-category-from-wordpress-and-woocommerce
 *
 * @param array  $args Array of arguments for registering a taxonomy.
 * @param string $taxonomy Taxonomy key.
 * @param array  $object_type Array of names of object types for the taxonomy.
 */
function cameronjonesweb_filter_taxonomy_args( $args, $taxonomy, $object_type ) {
	if ( 'category' === $taxonomy ) {
		$args['default_term'] = false;
	}
	return $args;
}

add_filter( 'register_taxonomy_args', 'cameronjonesweb_filter_taxonomy_args', 10, 3 );

cameronjonesweb-remove-default-categories.php

<?php
/**
 * Remove default terms from categories
 *
 * @link https://cameronjonesweb.com.au/blog/how-to-remove-the-uncategorised-category-from-wordpress-and-woocommerce
 *
 * @param array  $args Array of arguments for registering a taxonomy.
 * @param string $taxonomy Taxonomy key.
 * @param array  $object_type Array of names of object types for the taxonomy.
 */
function cameronjonesweb_filter_taxonomy_args( $args, $taxonomy, $object_type ) {
	if ( 'category' === $taxonomy || 'product_cat' === $taxonomy ) {
		$args['default_term'] = false;
	}
	return $args;
}

add_filter( 'register_taxonomy_args', 'cameronjonesweb_filter_taxonomy_args', 10, 3 );

/**
 * Delete the option setting for the default category
 */
function cameronjonesweb_delete_default_category_option() {
	if ( get_option( 'default_category' ) ) {
		delete_option( 'default_category' );
	}
	if ( get_option( 'default_product_cat' ) ) {
		delete_option( 'default_product_cat' );
	}
}

add_action( 'init', 'cameronjonesweb_delete_default_category_option' );