Shipping methods configured to display only certain postcodes do not appear
There are plugins that allow you to configure specific fields in the checkout. It is possible for customers to disable the native woocommerce postcode field and replace it with their own custom field.
As far as woocommerce is concerned, this custom field is not a postcode. While the native postcode field is disabled, any shipping address to determine the shipping method does NOT have a postcode, and for this reason no shipping method that is restricted to certain postcodes will match the shipping address.