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.
Now I definitely feel the grim reaper watching me age, knowing that's only 7 years away lol. Still remember when the movie first came out.