My prediction is that today was a 90 minute meeting and the next time they see each other will be in a year's time (if IG goes ahead) for another 90 minute meeting.
I think KC is motivated by thought of quietening his critics who say that he should forgive his son. He's the head of the CoE and has no moral high ground because of mistakes he made in his relationship with Diana so he values the chance to reduce his image of being a bad father.
I think the wider RF may also potentially benefit from a reduction in poisoned barbs coming there way from California. It's awkward for HAM's image to have tea and cakes and then sell more secrets.
W/C: I think they accept that it's up to KC to manage his relationship with his son. They'd never allow George to dictate their relationship with C or L. But they have said to KC - this needs to be low key, 100% private and absolutely no HIHO. Harry's foolishness is the extra evidence they need that he's completely unsuitable to represent the monarch ever again.
Although this week will have looked like HIHO to people not paying much attention (which is most of them, to be fair!), all the things that we've been discussing (IG being a bit of a dated format, his silly/political speeches, her merching her clothes and appearing on roundabouts to tiny 'crowds'), all of this is going to accelerate over the coming years. Today's 15 year olds probably have no memory of HAM being working royals. Time goes quickly and their public profile will inevitably get smaller. I reckon quite a lot of people in their 40s today would not be able to name Princess Margaret if they saw a picture of her when she was in her 50s, 60s, 70s. And she remained in the fold! This is Harry's destiny.
I think KC is taking a slow and steady approach which will end with him seeing them privately for a short time once a year.
I almost forgot to say what HAM get: they get their kids to have memories of meeting their grandfather the king which might be important to their profile in the future. An adult A / L being known for being related to the royals but having no memory of ever meeting any of them is less potentially lucrative than being able to say, 'ah, yes, I enjoyed my visits to see my illustrious ancestor. He had wonderful gardens, you know, bla, bla'. HAM themselves might be encouraged that their HIHO pretence has had a small boost but the news cycle moves on so quickly that it won't last.
Sorry, this turned into an essay!