I would separate this to a different filter operator. As of now, random[] is a math operator, and as such shouldn’t do listops. I’d rather extend the nth[] operator to take the parameter random or some such. Would be more semantic, I guess? Or something completely new like chooserandom[].
PS (next day): A new filter would have the option of returning a variable number of items from the list, like chooserandom[<numberOfItems>]. As one can see from the scrambler example above or the Lotto example in the plugin doc, removing an already chosen item from the list before choosing the next one is messy. That could be done much cleaner in JavaScript. An optional suffix like :all would return all items of the input list, but shuffled– it is the same as settting <numberOfItems> above to the total number of items in the input list, but without having to determine that number in advance.
Since all of this is difficult to do even with having a filter that returns a single random item as you proposed, a new filter with this additional functionality would actually cover a lot more usecases, like showing a random selection of neighbors when there are many.