From their perspective, I think KP is pretty happy with their strategy and are content with how it is playing out. From their perspective too, the strategy has worked out exactly the way they wanted it to. It is right and expected that not everyone would share their perspective or agree with their strategy but they are the ones with the skin in the game and it is their prerogative to do what they think is most beneficial for them not what others think.
BBC's analysis summarises their stance:
Analysis: A royal dilemma as public curiosity over Kate grows
Advisers to the Waleses are well aware of the online gossip - they read it, they chat about it, they know the conversation. But they stress that nothing has changed.
A spokesperson for Catherine brushed off social media speculation. "Kensington Palace made it clear in January the timelines of the princess's recovery. We said we'd only be providing significant updates. That guidance stands." There is, of course, the issue of privacy. For Prince William, protecting his wife while she recovers is paramount. Kensington Palace quite simply does not want the details of her health made public and aides feel no need to say anymore about it. But when Catherine does return to public duty the scrutiny will be intense. All eyes will be on her... Her team are well aware of the interest there will be in that moment so protecting her now has added importance. They will choose when and how we first see her in public again very carefully...
Yes, there is a clamour for information but "so be it" seems to be the mood. This is a princess who wants to keep things private.
Daily Beast's sources are even more explicit on their perspective that their strategy is working:
Royal Friends Dismiss ‘Toxic’ Kate Middleton Speculation
..
.However, friends of William and other royal sources told The Daily Beast the palace would not be pressured by “toxic” speculation into changing their carefully planned approach of saying as little as possible about the princess’ recovery.
One friend, asked about media commentary suggesting that the palace should be more open, such as an assertion in the Daily Mail that “by saying nothing, (the royals) invite speculation,” said: “The newspapers are always telling the family how to run their press operations. This time—surprise surprise—they seem to think it would be a good idea for the royal family to give them more information about Kate. William isn’t a big one for doing stuff because the Daily Mail says he should.”
A former royal staffer who still has friends and contacts inside the palace said: “Anyone who expects the palace to suddenly start giving lengthy updates on Kate will be disappointed. The principal aim of her being sequestered is to guard her privacy. I’m sure the press hate it because it is working. There is a really, really small bubble of people who know exactly what is going on.”
Indeed, the paucity of information made available to the media about Kate has been remarkable in and of itself...
The news blackout has been astonishingly successful, with almost nothing emerging apart from the very few crumbs of information the palace has sanctioned...
...While unfounded theories as to what is “really” going on” with Kate are ten a penny on social media, friends of the royal family are united in believing the truth is simpler and less dramatic. “They just want her to be able to recover in peace,” said another friend of the family. “The idea that they are going to be swayed by the idiots on social media saying she has been abducted by aliens is laughable.”
...The friend added that they had no special insight into Kate’s condition but said, “The whole world knows what’s ‘going on’ because they have actually been remarkably open: she had abdominal surgery, it went as planned, it wasn’t cancer, she is keeping to herself until after Easter and she is doing well. ‘Case closed’ in my humble opinion.”
Essentially, the speculation in the media is not a concern for KP neither do they see it as PR failure. KP is very adept at releasing captivating pictures and videos of the family. They don't need anyone to advise them re how to keep the public engaged. They have simply chosen not to do so and it is their prerogative. Similar with William's absence from a private family event. He has expressed his reasons to the stakeholders that matter, the Greek royal family. He does not owe the public any explanations. It is a family event not an official duty and he decided that 'personal matter' is how he chooses to couch the reason. His prerogative.
William is setting lines in the sand between his public life and his private life and setting out markers on how he chooses to live as a public leader. He doesn't take steers from members of the public or media, whether print, broadcast or social. He takes a considered view, assumes a stance, releases a statement and sticks to it whatever the fall out. Importantly, he takes any criticism on the chin, neither complaining or explaining. He will do what he thinks is right for him and his family; people are free to express their opinion about his actions in whatever way that suits them; he is also free not to acknowledge or respond to any of the expressed opinions. All parties exercise their freedom. A win-win.
In this age of over-sharing and social media pile-ons, it is a very counter-cultural approach and it takes a man of strong convictions and strong character to pull it off. He has now set the precedent that he will not be swayed by public/media pressure but will act based on his own convictions, wholly owning the consequences. This is how he chooses to live. Not everyone will agree with his actions and approach and that is fine too.
By all accounts, recent polling in the UK and US demonstrate that his strategy is working very well for them so far. We'll see how it plays out in the months to come.