A suspicious code in PQconnectPoll()

Hi

I find a suspicious code in libpq:PQconnectPoll(). I think it should be
fixed, but I could not produce a concrete problem.
What do you think about it?

I understand that PQconnectPoll() returns PGRES_POLLING_WRITING or
PGRES_POLLING_READ until state machine reaches terminal state(OK or BAD).
The return value indicates for users which event they should wait for
before next PQconnectPoll().
But PQconnectPoll() calls PQsendQuery("SHOW transaction_read_only")
in CONNECTION_AUTH_OK without returning PGRES_POLLING_WRITING before.

My idea is as following:

case CONNECTION_AWAITING_RESPONSE:
receive authetication OK, transit state machine to AUTH_OK and
return PGRES_POLLING_READING.

case CONNECTION_AUTH_OK:
clear any data from backend using PQisBusy(), transit to
CHECK_WRITABLE_STARTED(new state!), and return PGRES_POLLING_WRITING.

case CONNECTION_CHECK_WRITABLE_STARTED (new state!):
call PQsendQuery("SHOW transaction_read_only"), and transit to
CONNECTION_CHECK_WRITABLE, and return CONNECTION_CHECK_READING.

Regards
Ryo Matsumura