I'd say that state is actually easier to handle in functional languages. You just need the right abstractions for it.

I've been working with Phoenix lately, which basically just hands request/response details down a pipe of functions, which all can change the state of the response. There can be a lot of state contained in this response, but when you use Phoenix, you don't really notice it. The abstraction makes everything seamless - best web-framework I've used to date.