From a kind of spooky psychoanalytic view, the thing that makes conversation interesting is 'intersubjectivity', the experience of part of you becoming part of another person temporarily and then coming back home to roost. Our primary way of shaping ourselves, from that perspective, is not 'work on the self' directly, but comes about by having the self vicariously experience life from other perspectives.
I am largely a Montessorian, so my answer to 'why is X fun' is always either 'evolution' or 'personal development'. So what parts of having some conversations be more fun than others is evolutionarily or developmentally advantageous?
In this theory, 'intersubjectivity' is just interactive version of 'projective subjectivity', which is what you enjoy in reading, which is easier to analyze, because you choose it more for yourself. So I will go there, instead.
Enjoyment of reading does not seem to be about information, because reading stories is more interesting than reading informational texts most of the time, to the point where many informational texts are re-formed into stories to capture interest. Most people read fiction for characterization or for plot. So what makes a story more of a story and less of a stream of information is generally emotional or strategic alignment with the characters.
It seems clear to me that enjoying strategic alignment with the characters is about appreciating leadership and competence. It feels good to be inside the head of a person making good choices, because it teaches us how to make good choices, and it makes us want to consort with the kinds of people who do so, which is good for us. It feels good to be inside the head of a person making poor choices, because we can enjoy our realization that we could make better ones, and that we could help. It is an odd form of altruism, and validates our competence.
Enjoying emotional alignment validates the possibility of emotional alignment. We are always afraid of losing empathic connection with our broader circle of associations, for fear they will turn on us, or will not identify with us in crisis. By repeatedly experiencing empathy for people even farther removed from us, we allay that fear. At the same time we practice the skill of empathizing selectively, of knowing whom to align with, and whom to resist as a trap, a manipulator or an energy sink, which again, is good for us.