OP, I would mostly say it's the current royals on the throne.
This particular generation. Cash in bags/Noncing/Affairs/Racism etc. They constantly live under the shadow of the media exposing them, and have to throw titbits to keep certain things quiet.
They just have too many scandals.
Taking into consideration that both CPB&C don't have much charisma or are that well liked, they fear that the public would not be so forgiving if the rags dredge up everything in the background and constantly put it in front of our faces, the public would be fed up. This is the fear.
Enter the fab four. This link had to be severed by all means.
Already too many people (the public) have been asking for a pass on to W as it is. If not already taught, W has to make sure the same beneficiaries to his father's reign carry on being satisfied in future . But does W have any interest in that? His personality tells me not(though he may buckle under pressure), but he may not have a choice, and being Diana's boy ultimately, may not even have the stomach for it.
William with his relatable typical English looks and public school boy manners the UK loves and likes as representation (hence the movie stars, politicians and anyone who represents us).
Harry charming, 'naughty like us', 'ginger like those mocked', 'flawed like us', 'heart in his sleeve as we wish we could display', turns out dangerously decisive personality too.
KM looks great in fashion and her dimples is what we like as a representation of an English rose.
MM charisma, can do attitude, connecting us to both minority groups and foreigners.
Ah ah, the Fab Four was a lethal combination for the current royals. Imagine them all cozy, with H&M constantly whispering their 'do what's right' virtues in William's ear.
Anyway, back to your OP.
The RF are supposed to have a Comms Dept (preferably with a spokesperson/s) who put out proper statements and (preferably their face/s and name/s) like everyone else. Their stance was accepted because HMQE served for so long. But this would not be acceptable of any organisation, normally. Having a proper spokesperson means in general, no one believes all the other media except that person.
Ergo, I feel the RF just has too many skeletons in the closet, too much secrets for them not to feed the media.