would it really come to mind to someone who wants to hide to shut down the ACARS?
What you've failed to glean from news reports is that the ACARS sent a final message indicating the
active waypoint in the FMS had changed to one that gave the initial left-hand turn.
In other words, it had been programmed to turn by someone in the cockpit. This aircraft did not go into a heading mode. It was a deliberate, and premeditated turn, if the investigators' leaks to the media are to be believed.
This is why they know 'conclusively' that the airplane was hijacked/piloted on its rogue course.