In simple CRUD cases yes. In many other scenarios, you might not. If your insert is a select statement, with joins and clauses, you can easily insert too much data, or no data at all.
E.g.
CREATE TABLE t (id SERIAL PRIMARY KEY, x INTEGER UNIQUE);
INSERT INTO t (x) VALUES (42), (43) ON CONFLICT DO NOTHING RETURNING *;
I often use "insert into mytable(...) select ... from ... where ...", and I know I only want one row inserted.
In such cases checking that exactly one row was inserted is a very nice safeguard against buggy code/query, or in the freak case someone messed with the DB.