A decentralized solution removes the question who maintains a centralized database. That's important because, as you say, the answer to that question has always been the state. Which means it's never really been a question.
If you're cool with the government owning your identity -- and truly having the power to erase your entire existence, so they're not denying you any rights because there is no "you" -- then it doesn't matter. But for some people, it might matter to be able to point to something other than the mirror and say "I exist, and not just because I say I do. This matters because [this entity] is taking actions that are inconsistent with my existence and implied rights."
It's a small step, but it's one that opens up options that don't exist today.