If Carolina is to run a real search, it will never stay quiet. So if you don't announce HD's departure, once the rumors of us looking around start flying, it looks like we're working to replace him behind his back before we've discussed the situation with him.
Hell, the PTB can't even have a "private" discussion with the big money donors about HD's future without it becoming public and discussed.
College ADs have so many stakeholders involved in these decisions they inevitably leak like sieve. There's no way to do hardly any, much less all, of a coach replacement process in secret unless you cut out 98% of the typical stakeholders, which we can't do here. It's just not a feasible way to run things in our media-saturated time.