It's a common theme in mathematics to show an equivalence between two structures. We don't do it because it's fun, it's because if there exists an equivalence o

It's a common theme in mathematics to show an equivalence between two structures. We don't do it because it's fun, it's because if there exists an equivalence or some other relationship, we can use the existing body of work in one field in another. For example, group and ring theory often starts with the concept of symmetries, but it can then be shown, through an equivalence (or in mathematical terms, an isomorphism) that these have a relationship to polynomials. From that, we then easily show that there is no general formula for polynomials of degree greater than 5. Two vastly different fields, actually sharing something, and having a very useful result. Similarly for finite state machines and monoids. If you can express something as something else, you have the opportunity to shed light on it's structure and hence learn something new about it. Yes lots of things share that structure, it just so happens that monads are quite a general structure, that doesn't mean that no interesting results are attached to them.