This is not true. The arguments for `next` include both:

* The target stream.

* A "state token" or universe.

You get different results with different state tokens.

At a high level, the thing to consider is that we can model all imperative programming with functional programming -- we can model Turing Machines with Lambda Calculus -- as well as go the other way around, because Turing Machines and the Lambda Calculus are, for all intents and purposes, equivalently expressive.

Modeling IO with state monads isn't a hack; it's the point.

Can you replay a get from stream by passing in an older token?

Monads provide a way to combine them and a way to inject values into them; but not all monads provide the inspection interface that would allow you to examine that state token. The definition of a monad guarantees only the injection and the combination (the "unit" and "multiply").

  next :: Stream a -> IO a

You can perceive yourself moment ago exactly because of that.

Others who have not seen you recently hold the old reference to you.

I would rather say that the world is naturally immutable.

That's not how IO in Haskell works, you're basically describing what Haskell would be if it literally had no side-effects ever.