I host one on my phone, that fetches notes from my frens and allows me to read and write notes on the train (spotty Internet). But I don't see the use case for exposing it to some wider network. That would raise the load in the phone, after all.

I entirely agree on this one. I'm someone who likes explicit control over my firewall and incoming/outgoing connections. I wouldn't want to be connecting to a bunch of random servers (relays), you never know which ones could poison your device. One buffer overflow in the client code (meaning the websocket client library or parsing code itself) and you have a RCE vulnerability. The same goes for incoming connections. I assume there is a localhost optimization.

You lack imagination. You could run an old Android phone as a cheap & easy self hosted relay. Self hosted DMs over Tor, leaving no trace of your messages on large relays. Android is transitioning to be a desktop OS as well, making the power issues of phone use less of an issue. It's basically the same as nostr-relay-tray with the proxy settings enabled. I've been running that for a few days as well, it makes a fine outbox relay.