The immediate use for this that jumps out at me is batch processing: you take n inputs and return n outputs, where output[i] is the result of processing input[i]. You cannot throw since you still have to process all of the valid input.
This style also works for an actor model: loosely coupled operations which take an input message and emit an output message for the next actor in the chain. If you want to be able to throw an exception or terminate prematurely, you would have to configure an error sink shared by all of the actors and to get the result of an operation, you so have to watch for messages on both the final actor and the error sink.