Yes, this is exactly the distinction I was struggling to articulate.

“Online” has collapsed into a single bucket that includes friends-only play, strangers, stores, chat, downloads, etc. What I want (and what you’re describing with running servers) is a way to scope online access: friends-only communication, no discovery, no stores, no strangers.

The frustrating part is that many platforms either (a) force these things to come as a bundle, so saying “yes” to playing with friends implicitly says “yes” to a much larger surface area; or (b) make the unbundling process so complex that well-meaning parents fail and exhausted parents give up.

jonathaneunice put the incentives behind this more sharply than I did here: https://news.ycombinator.com/item?id=46465547