I think ISubject<I,O> has the interface for a pipe, with IObservable being a Producer equivalent, and IObserver being a Consumer equivalent. So there may be some cunning that could be done with your own implementations [to create an Effect]. (This is just wild brainstorming without looking at the code, so take all of this with a large pinch of salt).
Working within the Rx system, there'd be two ways of doing this:
The Observable has a mechanism for slowing down, but obviously it can't get instruction from observers - so it would have to make a judgment on what is 'too much'; a slow down would affect all observers. Definitely (well probably) not what you want.
The other way is to use the various buffering functions in Rx on the subscription, or roll your own function that has some intelligence. That localises the 'backing up' on a per observer basis, but doesn't slow down the observable itself.
To 'Stop' you could switch your subscription to Observable.Never<T> until you're ready to receive messages. Obviously you'll miss messages generated on the other stream whilst you were not listening.
I think it is relevant, what allows you to ignore the behavior of the system in favor of a component?
Dean wampler in a recent talk spoke of "Reactive Streams" which add this capability, but I have not seen it yet.
I have not seen anyone do this in Rx yet. Also ideally the back pressure is out of band to avoid starvation of that channel
Or do you think it should be an inherent feature of the stream itself? Isn't the point of IObservable to be the dual of IEnumerable, so calling Select on IEnumerable is a projection from A -> B, calling Select on IObservable is also a projection from A -> B, I think having an additional effect breaks that duality. So an Observable that has a side-channel or out-of-band stream wouldn't be an Observable, it'd be another category (which is why I suggested Pipes).
I totally understand why you'd want something like that, I'm just not sure it's fair to suggest Rx has design mistakes because of this though.