Does SELECT INTO is affected by default_tablespace?

According to my test, it does not:

test=# set default_tablespace = testsp;
SET
test=# create table a (i int);
CREATE TABLE
test=# select * into b from a;
SELECT
test=# \d+ b
Table "public.b"
Column | Type | Modifiers | Description
--------+---------+-----------+-------------
i | integer | |
Has OIDs: yes

test=# \d+ a
Table "public.a"
Column | Type | Modifiers | Description
--------+---------+-----------+-------------
i | integer | |
Has OIDs: yes
Tablespace: "testsp"

If so, shall we fix it?

Regards,
Qingqing