Of course you're right, but I think a function like

    Complex -> Radian -> Complex

offers two points of view. You can see it as a function which transforms complex numbers or a function representing an update to the internal state of a Complex object. The second highlights the need to keep track of identity. Throwing an STRef into the mix just gives you a particular kind of history—one which only retains the "now".

Which is all sort of obvious and meaningless, but I still think it's interesting to think about. I think coalgebras tend to force thinking in terms of identity in this kind of way.