I do think a designated relay for “private” events would be useful.
For what it’s worth, I’m happy to also build truly “individual” inbox relays that accept all kinds and work exactly as you have in mind nostr:npub1acg6thl5psv62405rljzkj8spesceyfz2c32udakc2ak0dmvfeyse9p35c but I don’t expect many users to run their own. If they did, I have to assume speed and uptime would be poor on average making the client experience worse for everyone. I guess I’m not totally sold on the tradeoffs, personally.
We could offer it as a paid service (where we host them), but then are we really accomplishing anything by doing so?