Show only free / $0 shipping methods when available

wc-hide-non-free-shipping.php

<?php // only copy if needed

/**
 * Hides any non-free shipping methods if free shipping is available
 * 
 * @param array $rates array of \WC_Shipping_Rate objects that apply to the cart
 * @return array - the updated available rates
 */
function sww_wc_hide_non_free_shipping( $rates ) {

	$free_rates = array();

	foreach ( $rates as $rate_id => $rate ) {
		
		if ( 0 === (int) $rate->cost ) {
			$free_rates[ $rate_id ] = $rate;
			// uncomment this `break;` if you only want to show the first free rate
			// break;
		}
	}

	return ! empty( $free_rates ) ? $free_rates : $rates;
}
add_filter( 'woocommerce_package_rates', 'sww_wc_hide_non_free_shipping' );