If you want something hosted with full privacy, yet importable in the standard calendar apps, then I don't think you'll find anything for the time being.
Protonmail and tutanota both provide full privacy and are hosted options, but they require their own apps since they want to ensure reliable E2EE. I suppose you either need to re-evaltuate your requirements or wait for a suiitable product to be launched.
From their site: All of our payment methods are anonymised using a payment system developed by Posteo. We do not link payment information with email accounts.
Maybe buying a single seat enterprise license of Microsoft365 might work for you. Microsoft treats enterprise clients very differently than end users. Only (potential) down side is that you will have to set your own security policies and manage a bunch of things that go beyond a calendar. There is a bonus though. A single enterprise seat license includes 1TB of private-ish enterprise cloud storage.
I tried this and found that at the time there were massive limitations. Admittedly it was a few years ago, but they didn't make it simple to just have a forwarding mail group so that I could have a shared mail address/distribution list to myself and my wife forwarded to our inbox, and you basically had to have a shared email box that was separate to your primary. It didn't pass the spouse test considering this is a basic feature that everyone has so it didn't make it past the trial.
I was actually surprised at how limited the 365 was, I don't remember the other limitations but they seemed fundamental.
Yes, it could very well fullfil my requirements, but preferably a bit more simplistic. Like Proton Calendar, if only it integrated into the iOS ecosystem.
Idea #2. Why not just use apple’s iCloud with advanced data protection turned on? It’s not perfect from a privacy perspective but at least apples business model isn’t data mining you.
It sounds like EteSync is exactly what you're looking for. A hosted NextCloud instance + DAVx5 is admittedly a bit lacking in the "full privacy" department, and Proton or Tutanota doesn't integate with the standard calendars, but both would also be valid options IMHO.
Unless referring to encryption, can you expand on why NC with Dav isn't private? I've got both selfhosted (in home) and haven't picked up on any traffic sharing my calendar to third parties through my logs and alerts, so would like to know more of what you've seen to see if I have a gap in my automated alerts.
Edit: unless your answer was just in response to the OP wanting an already hosted system, then yeah I can understand what you mean there.
Ich betreibe (kommerziell) einen davical Server. Da läuft sogo als web interface und mit davx5 kannst du das komplett offen und per https auf jedes android device syncen. Funktioniert seit Jahren zuverlässig und kostet nicht die Welt.