door() ->
      | :open(:close)
      | :closed(:open | :lock)
      | :locked(:unlock)

What feels wrong to me in this example is that the type system doesn’t “know” that :close-ing an :open door will yield :closed. Expressed as a state diagram, it would only have a single node, whose type would be a sum type with three options, and the diagram doesn’t tell you which option you end up with for any given state transition, while at the same time you have to know the current option to know which transition you may take from the current state.

So there is an asymmetry regarding the associations to the three sub-states between the two ends of a state transition. Or in other words, the state transition arrows begin in three different states but end in a single state that is the opaque combination of the three source states.