A lot of web frameworks enforce the shared-not-that-much (not quire "shared nothing", but close) style of programming where every HTTP request is essentially just an "event" that hooks into a controller-handler? And if you want anything to stick around from one request to the next, you keep it in memcache/db/BaaS/third-party service, not your own process?
I don't think this is as radical a shift as many here might think, especially given the move to containers is already well underway.