I think it's unfair to dismiss the disappointment of people who were hoping for a public appearance. Besides the press, there were a lot of ordinary people who went to the Lindo Wing to see the Cambridge babies in person and "feel a part of the joy of a new baby".
And that's not unreasonable to want, because as much as these two humans as "Meghan and Harry" are private people, they also embody the Duke and Duchess of Sussex and exist within a particular structure of mutual obligations. The nation agrees that the Duke and Duchess are able to live *very* comfortably in beautiful surroundings, do relatively little work compared to the average Joe working a 40-60 hour work week, and largely pursue things that interest them. In return, the Duke and Duchess, as part of the institution of the monarchy, exist as symbols for the nation; they pursue philanthropic issues and there is a very reasonable expectation that they be seen. So yes, if the average Londoner was really hoping to go to the hospital and demonstrate their support and joy for the new baby, it's churlish to completely deny them a sense of disappointment.
"Meghan and Harry" will always be in conflict with "The Duke and Duchess of Sussex". That's just part of the bargain.
Maybe this is an effort to deny the press their crazed coverage. But the people who're actually going to be saddened by this will be the average people who just wish Harry and Meghan happy, and I think that's a bit sad.