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By CNN Royal Correspondent Max Foster and Lauren Said-Moorhouse in London

Alberto Pezzali/AP

As King Charles III waved to well-wishers outside the hospital and Queen Camilla stood by his side, both smiled broadly at the cheering crowds. The message they hoped to convey after the family's double health scare was clear: The crown is still strong. 

The 75-year-old monarch left a private hospital, the London Clinic, on Monday afternoon. Hours earlier, a car full of flowers for the King's daughter-in-law, Catherine, was seen being driven away from the same hospital. But no sign of the Princess of Wales, who departed out of sight of the cameras. 

There is a long tradition of royals appearing outside hospitals to reassure the public. The fact that Charles did so but Kate did not has become a talking point. She has made these public appearances before, such as after the birth of her children, but she opted to slip away on this occasion. 

The palace has been fiercely protective of the Princess of Wales, making clear in statements that she deserves some privacy. Aides understand she is popular and that her fans will have hoped to catch a glimpse of their favorite royal as she left, especially as she isn't expected to reemerge for several months. 

But there could be a simple explanation for her absence in that she may simply not be feeling ready to smile for the cameras yet. While we know her operation was successful, we don't know exactly what it was for. 

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Both Buckingham Palace and Kensington Palace issued statements on behalf of the royals, expressing their gratitude for the kind messages the family has received during their hospital stays. 

Charles will now be out of the public eye for a "period of private recuperation" at an undisclosed home. Meanwhile, a spokesperson for the Princess of Wales said she is "making good progress" and now continues her recovery in Windsor. 

Both Kate and her husband, Prince William, have cleared their schedule of public duties until at least Easter. 

The recent, unusually candid, health updates have been welcomed by some as a signal of a slightly evolving and more transparent monarchy. 

But with three of the most senior members of the family sidelined, a difficult reality has been laid bare: The family is incredibly stretched.
 
The number of public-facing "working royals" has dwindled in recent years as "the Firm" sought to rebrand in step with the times. Only working royals carry out engagements on behalf of the King, splitting the 2,710 visits and events undertaken last year between them. 

That group was supposed to consist of 14 family members: King Charles, Queen Camilla, Princess Anne, Prince Andrew, the Duke and Duchess of Edinburgh, the Waleses, Sussexes, the Duke and Duchess of Gloucester and the Duke and Duchess of Kent. 

That is, until Prince Harry and Meghan chose to step down and Andrew was forced to, in the light of his relationship with the late pedophile Jeffrey Epstein. Now we have 11 - more than half of whom are over the age of 70. 

The monarchy over the years has been under pressure to reduce expenditure and reflect a nation currently undergoing a cost-of-living crisis. Charles' accession came amid a new era of fewer royals  carrying out more engagements.

"We have a much smaller royal family going into 2024 - much fewer royals to do the engagements because we have an aging King," CNN historian Kate Williams says. "It is really all falling on William and Kate, Edward and Sophie and Anne. And when one or more of them is out of action, that is quite a significant impact on the royal family." 

Until Charles, Kate and William return, Camilla will be the most senior public face of the British monarchy, with just seven others backing her up. 

The Queen has over the past two weeks significantly increased the number of engagements she is undertaking but there are only so many hours in a day. Some have wondered if it would be helpful to fold Princesses Beatrice and Eugenie into the core group. After all, they did occasionally support the late Queen Elizabeth II at engagements. 

What this period has shown is that, while Britain's royals are an institution, they are also a normal family susceptible to everyday human frailties - and that could be something the King may want to address in the future. 

King Charles' diagnosis raised awareness of prostate condition. What are the warning signs?

Max Mumby/Indigo/Getty Images

Everyone has experienced the urge. You're in your car on a road trip when you suddenly feel a strong pressure in your bladder. The need to pee necessitates a rush to a rest-stop bathroom. Such urges can even happen at night, disrupting vital sleep.

This rush is something that King Charles III might have encountered prior to his decision to undergo prostate surgery.

Find out more on CNN Health.

'Better Call Saul' star discovers he's related to the King.

Getty Images

Bob Odenkirk was royally amused to find out he has a famous relative. During an appearance on "Finding Your Roots" that aired on PBS Tuesday, host Henry Louis Gates Jr. let Odenkirk know he was related to the British aristocracy. "That is wild," the "Better Call Saul" star said. But it got even wilder when he was also told about his connection to the British King.

Read our story here.

Keld Navntoft/Scanpix Denmark/AFP/Getty Images

A painting by Denmark's former monarch, Queen Margrethe II, is going up for auction.

Works by the 83-year-old Queen, who is a prolific artist, have featured in various exhibitions, but the opportunity to buy one of her paintings is rare, according to a statement from Bruun Rasmussen auction house published Tuesday.

"You now have the opportunity to acquire a very special - and not least royal - work of art," said the auction house, which has set an estimate of 75,000-100,000 Danish kroner ($11,000-$15,000).

Read more on CNN Style. 

Kirsty Wigglesworth/Pool/AFP via Getty Images

Glenn Bartley, head of the Royal Bindery, shows a miniature book, written by Queen Camilla, during a reception for authors, illustrators and binders who have been involved in the new Miniature Library collection for Queen Mary's Dolls' House at Windsor Castle.

"Holocaust Memorial Day offers a valuable opportunity for the richly diverse communities of this nation to come together and recommit to building a society free from antisemitism, persecution and hatred."

– King Charles III

The monarch may have been going in for his treatment last Friday but he made sure to send a message ahead of Holocaust Memorial Day on Saturday.