I think the main class of problems it solves is it lets multiple applications, which may be developed by completely different entities at different times, share data with very strong guarantees.

So in the context of the Web Revivalist movement, how do you build stateful applications? It's great when individuals host their own DIY servers, but that doesn't really give you much stability. And in aggregate, it's even more difficult to build rich, stateful ecosystems of applications. How do you handle servers going down and APIs changing? Link rot for stateless websites is a hard enough as it is.