It seems I am able to delete the default Customer Billing Profile field for the Order Entity.
Without it the commerce (checkout) is broken.
The website encountered an unexpected error. Please try again later.
EntityMetadataWrapperException: Unknown data property commerce_customer_billing. in EntityStructureWrapper->getPropertyInfo() (line 339 of drupal_path/sites/all/modules/contrib/entity/includes/entity.wrapper.inc).
Shouldn't be locked somehow?