I think this is the goal of ENS (https://ens.domains/)? But they screwed the pooch by not linking it with the extant DNS system.
In reality, even though we’ve been shown (by, eg, Twitter) how depending upon a third-party namespace as a source of your identity is a bad idea, I think as long as you do enough due diligence on the top-level registrar, “owning” your own DNS domain is sufficient for most people for most purposes.
The real way to do it is public/private keypairs (… pointing to a content-addressable linktree-like thing for actual contact details) but then the problem is key management as you rightly point out. You can indeed be self-sovereign if you’re willing to take on the responsibility of not losing your keys but again, the best tradeoff for most people is for Apple and Google to do it for them via their phones and associated cloud backup services.