What makes them reusable is dependent on how you implement them.

A state machine that is the simple relation:

(state, event) => [state', actions]

has a very reusable interface, as long as it doesn't execute the actions (effects, commands, etc.) itself. It's just a pure function that can be used anywhere to get the next state and the actions to execute as a result of receiving an event.

Then you can do exactly what you're describing: connect the wires, style the components according to state, etc.