[qrmn]

Impossible is a strong word - one prefers to reserve that for provably doomed problems like DRM - but several common, simple paradigms do present an unexpected technical challenge, or even an open research problem, or need to be expressed slightly differently to be practical, in a distributed, privacy-preserving, untrusted-server kind of model.

For example, paraphrasing quite a lot - uniqueness of names requires ordering; ordering probably requires consensus; consensus has a Sybil problem for which some kind of countermeasure is needed. So a namespacing problem that seems simple, and is simple in a centralised/trusted context, may only be practical to solve with a blockchain-like structure with a computationally-heavy proof-of-work in a distributed trust architecture. Even that may still be vulnerable to attacks from someone who can outcompute the rest of the network: and a Nation State Adversary (as a friend snarkily puts it) may actually have enough budget to try that. There may be another way, but maybe not another way that satisfies all the security requirements or that would survive an attack. And there are still other niches you need to worry about, like homoglyph attacks.

That's a long way to go just to make sure that there aren't two ~bobs! So you end up thinking, maybe it's better to find another way that ~alice knows she's talking to the right ~bob? Then you have rephrased your security problem as more of a UX problem: how do I try to avoid impersonation? - which is perhaps more practical to solve another way. [Edit: Also, now your users won't have to fight over who gets to take ~bob first. This may or may not be an advantage, depending on how you feel about username exclusivity.]

It's going to require a lot of hard work to solve this type of problem comprehensively; in the meantime, Signal does more or less the best we can do practically right now, and there's a lot of value in a practical solution that's best-in-class, works and millions of people can just pick up and use now.