I mean, for which problems does a true, Fielding-style RESTful API and universal client model actually make sense?
Fielding himself was describing the World Wide Web. Not a web application - he was talking about the entire ecosystem on which arbitrary web applications can be built.
The web (when driven through a web browser, at least) is RESTful, no matter what you do on top of it.
If you are not building your own universal application ecosystem of services and clients akin to browsers and web servers, you don’t actually need a REST architecture. You probably need an RPC architecture.
But for some reason people have acquired a vague understanding that REST is ‘better’ than RPC.
What they usually mean is that idempotent resource-verb based RPC APIs are a more compatible way of building applications within the REST architecture of the web than SOAP-like RPC APIs are.