If I could predict every aspect of every flight that might generate PAO/MSM/public interest I'd be putting that power to much better use.
There is a real limit to practicality when it comes to trying to provide a PAO with enough information on every single flight, especially now that taskings and scheduling are moving to systems to which they have no access. Most of them would not have a clue about the information anyway. If they receive a question, they should know whom to ask in turn.
An anecdotal tale:
In the Good Old Days, we used to have PA systems for Kiowas and Twin Hueys. These were semi-directional, and, as can be imagined, quite loud. There was an annual currency requirement, as there was/is on most mission kits and flying sequences. We could, of course, meet that by flogging around the range and training area for two hours taking turns endlessly saying "Test one two three test one two three", or, we could provide a little return to the local population. We began to schedule these missions in mid- to late-December, and would float around Petawawa, Pembroke, Chalk River, Deep River at a couple of thousand feet and play Christmas Carols. Most people could not tell from where the music was coming, as it would fade in and out, but feedback was universally positive - until one Grinch complained about the "waste of taxpayers' money" to the local MP's secretary.
Unlike armoured vehicles, aircraft need to go to places and do things along the way. There is a lot of latitude there, so long as the training requirements are met. There is little value in conducting instrument approaches at one's own base, for example, as they are quickly committed to memory. There are generally few airports in close proximity that offer variety, so, to gain that experience and to practice IFR cross-country flight, longer-range overnight away trips are scheduled as necessary. Crews can choose where they wish to spend a night. They can do that at somebody's hometown, or a city that has something interesting to offer in the evenings, or they can be forced to go to somewhere with nothing just to be miserable. Cost to the public purse is the same either way, but highly-trained aircrew that represent a significant public investment have one less reason to stay in a job that pays significantly less than could be made elsewhere.
As for the Griffon in question lately, that crew and machine could have flown a two-hour currency flight and the helicopter spent the rest of the day sitting in the hangar and the crew cooling their heels in their office, or that flight could have involved an intermission of a couple of hours sitting on the ground while a few fishing rods were put to good use. Cost to the public purse is, again, exactly the same. Training value is, again, exactly the same. A crew, again, receives a little more motivation towards their jobs. So longs as the unit can cover its standby requirement, other training can and will be conducted.
Effort put into teaching all CF pers about OPSEC and Facebook, etcetera, would be far more valuable than effort put into teaching PAOs about every aspect of flying ops - and not for coverup purposes.