Nor would it constitute a "striking feature" of special relativity.
Please, please, please read the page you linked.
Are you telling me to reread this part:
By itself, this single use of the ansible doesn't create a causality violation. If Bob transmits a signal back towards Alice using a conventional light-speed transmitter, she receives it a later time than when she signalled to Bob. Even if Bob re-transmits with his ansible, Alice receives the reply just a little after she sent out her signal. The problems arise when we bring another inertial frame into play.
Either tell me what I'm misreading or tell me why it's wrong!