Apart from that, I think per-service identities are the best that can be hoped for. If I choose to engage with Facebook, I have to trust them to some extent anyway, so trusting them with my identity on Facebook is probably good enough. If I want to establish that some Twitter identity is the same as some Instagram identity, I can do so by directly referencing them from one another. I don't think we can do much better than that without involving the state.
And there’s already at least one blockchain purpose-built for naming - https://handshake.org/. Worth reading their design notes on how and why it works as it does.