I wonder what they're doing with PP that they couldn't do in Windsor? I noticed during the crown King George vi had surgery in Buckingham Palace.
I'm quite certain they could do that nowadays as well, they had full on operating theatres for k G VI and also for Liz during labour (in case something went wrong, a fully functional op was set up in the next room!).
I think they go to hospital nowadays instead of staying home because of logistics and PR. It's just easier to be in a hospital where all the medical staff and equipment is, than for medical staff to leave their main base for one patient and have all of it set up at home. And whatever may go wrong, docs and nurses are immediately on hand instead of being called in (by which time it might be too late). On top of that, imagine the public outcry for this. Docs for you, but not for anyone else?!
I don't think this points necessarily to a bad situation, he was in hospital in the past years for something as "simple" as a urinary tract infection. I do believe the palace statement that it is just to be safe, it makes perfect sense, at his age you don't want to risk anything, the body doesn't heal as easily or quickly anymore, you can't call docs and nurses to your home out of frankly selfishness and they have the money for a top notch private hospital which is amazingly equipped. The rooms look like home with sofas etc.
Even during this pandemic, the Ed VII hospital is fairly safe, it's private and doesn't treat Covid patients and it has only about 57 beds.
I have wondered a few times why the Ssexes moved to the US. Sure, they have the money for healthcare and schooling not to be an issue, but it's so far away and they moved when the pandemic was ongoing. Meg might want just her mum in her life, but H has elderly grandparents who are at record age and an elderly father. Even before the pandemic, money aside, you hop on the next possible plane, but you're still taking almost a whole day to get home, which is freakishly long in situations like now, plus the jetlag. They could've scuttled off in the UK to lead a quiet life or another European country. This would've still made it possible to register their foundation in scam paradise Delaware.
As bad as UK press is (and it's world wide renown for all that's wrong with it, it's literally part of the English curriculum abroad!!), they were still better protected in some ways in the UK than they are in the US.