This entire system seems very stateful.
Also, in the real world, requests to one web service end up cascading out to multiple web services, with differing permissions models. For example user comes in with a token, makes a request to a web service, which then has its own secret store that it fetches an API key from to make a request to another web service.
Very rarely in life has it been as simple as "fetch data from this API". It is "fetch data from this API given this auth token and that API takes that auth token and uses it to get another auth token, attaches some tracing info for diagnostics in case things go wrong, writes some metrics to a DB so the team can track API usage, then goes out to a couple more services, gets data from them, collates it, and eventually gives some data back to the user."
The system we describe in the talk is indeed stateful, but it's worth pointing out that the Photon runtime is referentially transparent in the pure functional programming sense. People think functional programming is about avoiding state and effects; it's not. It's about gaining control over our effects so that we can orchestrate scaled up fabrics of millions of fine grained effects without loss of composition, reasoning or control. This is the promise of modern functional effect systems, and is the underpinning abstraction that powers Photon.
There's room for so many different solutions to so many different problems. Shooting something down because its "stateful" well, okay if you know your problem domain well and that's significant to you then so be it, but that smells to me like "I have nothing valuable to contribute so I'm going to throw out a meaningless non-sequitur". I'll happily prioritize developer productivity first when user experience is not meaningfully impacted. I suspect that ~95% of web developers are in that same position.
"Could", of course, is the operative word! But given that we have to manage state now anyway, this seems like an approach with a lot of potential.