Base tables that have a surrogate key and all its unique constraints have an optional column

Copy SQL

WITH unique_columns AS (SELECT 
  n.nspname AS table_schema,
  c2.relname AS table_name,
  a.attname AS column_name,
  c.relname AS index_name
FROM 
  pg_catalog.pg_class AS c INNER JOIN pg_catalog.pg_index AS i ON i.indexrelid = c.oid
  INNER JOIN pg_catalog.pg_class AS c2  ON i.indrelid = c2.oid
  INNER JOIN pg_catalog.pg_namespace AS n ON c.relnamespace = n.oid
  INNER JOIN pg_catalog.pg_authid AS u ON  n.nspowner = u.oid
  INNER JOIN pg_catalog.pg_attribute AS a ON a.attrelid = c.oid    
WHERE c.relkind = 'i'
AND i.indisunique=TRUE
AND i.indisprimary=FALSE
AND a.attnum>=1
AND a.attisdropped = FALSE
AND (n.nspname = 'public'
	 OR u.rolname <> 'postgres')),
all_unique_constraints_have_optional_columns AS 
(SELECT A.table_schema, A.table_name
FROM unique_columns AS U INNER JOIN information_schema.columns A USING (table_schema, table_name, column_name)
INNER JOIN information_schema.tables T USING (table_schema, table_name)
INNER JOIN information_schema.schemata S ON A.table_schema=S.schema_name
WHERE T.table_type='BASE TABLE'
AND (A.table_schema = 'public'
OR S.schema_owner<>'postgres')
AND A.is_nullable='YES'
GROUP BY  A.table_schema, A.table_name
HAVING Count(DISTINCT index_name)=(SELECT Count(DISTINCT index_name) AS cnt FROM unique_columns AS u WHERE u.table_schema=A.table_schema AND u.table_name=A.table_name)),
tables_with_surrogate AS (SELECT c.table_schema, c.table_name , c.column_name
FROM information_schema.columns c
LEFT JOIN information_schema.domains d USING (domain_schema, domain_name)
INNER JOIN information_schema.schemata s
ON c.table_schema=s.schema_name
WHERE (coalesce (c.column_default, d.domain_default) ILIKE '%nextval%' OR c.is_identity='YES')
AND c.is_nullable='NO'
AND table_schema NOT IN (SELECT schema_name
FROM INFORMATION_SCHEMA.schemata
WHERE schema_name<>'public' AND
schema_owner='postgres' AND schema_name IS NOT NULL))
SELECT table_schema, table_name
FROM tables_with_surrogate AS ts
WHERE EXISTS (SELECT *
FROM all_unique_constraints_have_optional_columns AS au
WHERE ts.table_schema=au.table_schema
AND ts.table_name=au.table_name)
ORDER BY table_schema, table_name ;