WooCommerce Distance Rate Shipping: Filter to only return the shipping rate with the lowest cost when multiple rates are available.

filter-distance-rate-shipping-by-lowest-cost.php

add_filter( 'woocommerce_package_rates', 'keep_only_lowest_distance_rate', 20, 2 );

function keep_only_lowest_distance_rate( $rates, $package ) {
    $lowest_rate_key = '';
    $lowest_cost = null;

    foreach ( $rates as $rate_key => $rate ) {
        if ( is_null( $lowest_cost ) || floatval( $rate->cost ) < $lowest_cost ) {
            $lowest_cost = floatval( $rate->cost );
            $lowest_rate_key = $rate_key;
        }
    }

    // Keep only the cheapest one
    foreach ( $rates as $rate_key => $rate ) {
        if ( $rate_key !== $lowest_rate_key ) {
            unset( $rates[ $rate_key ] );
        }
    }

    return $rates;
}