Security through obscurity would probably cover most needs for me, with a few password protected and private posts. Although, I don’t know how logistically in WordPress to not include a specific post in the feed — that would work for pages where you just don’t add it to the menu and make it a hard-to-guess URL, but not posts.
I think people are starting to see and get used to the concept of private posts, with services like Patreon and Substack offering subscriber-only content — I think the paid subscriber concept would translate well to explaining to a friend or family member why they might need to be granted permission / to log into someone’s website to read certain kinds of content.
Question to ponder: what happens to my website after I die? As Chris pointed out, it’s not just a matter of paying hosting, but also the “admin tax” of installing updates and managing security. It would be horrible to have your website taken over and turned into a spam / spyware site after your death!
I could see a service that migrates your website to a new managed hosting, and also sets up a “memorial” page on the site like people seem to use Facebook posts for, with someone to manage webmentions / comments.