A possible alternative to the initial solution in WooCommerce PR#37847 (relates to this comment: https://github.com/woocommerce/woocommerce/pull/37847#issuecomment-1542940612)

pr37847-alt__shipping-flat-rate-class-handling.diff

diff --git a/plugins/woocommerce/includes/shipping/flat-rate/class-wc-shipping-flat-rate.php b/plugins/woocommerce/includes/shipping/flat-rate/class-wc-shipping-flat-rate.php
index 4b140a814f..5719a8a12b 100644
--- a/plugins/woocommerce/includes/shipping/flat-rate/class-wc-shipping-flat-rate.php
+++ b/plugins/woocommerce/includes/shipping/flat-rate/class-wc-shipping-flat-rate.php
@@ -177,8 +177,16 @@ class WC_Shipping_Flat_Rate extends WC_Shipping_Method {
 				// Also handles BW compatibility when slugs were used instead of ids.
 				$shipping_class_term = get_term_by( 'slug', $shipping_class, 'product_shipping_class' );
 				$class_cost_string   = $shipping_class_term && $shipping_class_term->term_id ? $this->get_option( 'class_cost_' . $shipping_class_term->term_id, $this->get_option( 'class_cost_' . $shipping_class, '' ) ) : $this->get_option( 'no_class_cost', '' );
-
-				if ( '' === $class_cost_string ) {
+				$no_class_cost       = 0 === strlen( $class_cost_string );
+
+				if ( $no_class_cost && 'class' === $this->type ) {
+					// If we are calculating per each individual shipping class, but one of the products belongs to a class
+					// for which a cost has not been defined, then we cannot supply a shipping rate.
+					$has_costs = false;
+					break;
+				} elseif ( $no_class_cost ) {
+					// Otherwise, if we do not have a class cost but we are intending to use the highest available rate,
+					// we should simply skip this product.
 					continue;
 				}