Postgresql – Postgres role does not inherit permissions of superuser role via membership in that role

In the snippet below, the role writer is a member of a superuser role named admin. The admin role can insert rows into a table but the writer role cannot insert rows into the same table. Why does the writer role not inherit permissions from the superuser role admin?

CREATE TABLE test_check_roles( id SERIAL NOT NULL );
CREATE ROLE admin SUPERUSER LOGIN;

-- Insert succeeds as the admin role.
SET ROLE admin;
INSERT INTO test_check_roles (id) VALUES (DEFAULT);

-- Insert fails as the writer role with:
--   ERROR:  permission denied for table test_check_roles
CREATE ROLE writer LOGIN INHERIT;
GRANT admin TO writer;
SET ROLE writer;
INSERT INTO test_check_roles (id) VALUES (DEFAULT);

Based on the documentation below (Postgres 12 – Role Membership), I expected writer to have all privileges of the admin user since the writer role has the INHERIT tag.

Member roles that have the INHERIT attribute automatically have use of the privileges of roles of which they are members, including any privileges inherited by those roles.

Reproducible example

docker run --name pg-test -d --rm \
    --env POSTGRES_HOST_AUTH_METHOD=trust \
    -p 54321:5432 \
    postgres:12.2

psql -h localhost -p 54321 -U postgres -d postgres \
    -c "CREATE TABLE test_check_roles( id SERIAL NOT NULL )" \
    -c "CREATE ROLE admin SUPERUSER LOGIN" \
    -c "SET ROLE admin" \
    -c "INSERT INTO test_check_roles (id) VALUES (DEFAULT)" \
    -c "CREATE ROLE writer LOGIN INHERIT" \
    -c "GRANT admin TO writer" \
    -c "SET ROLE writer" \
    -c "INSERT INTO test_check_roles (id) VALUES (DEFAULT)"

docker stop pg-test

Related questions

• Postgres role permission problem: Related to ALTER DEFAULT PRIVILEGES.
• Why is a new user allowed to create a table? – Has a good answer describing that privileges aren't hierarchial.

Observations

If I run CREATE TABLE as the admin role instead of the postgres role, the example works. It seems the permission are somewhere lost between postgres owning the table, the admin having superuser, and writer being a member of admin. I don't follow why a table created by the postgres role is accessible by admin by not by writer.