State machines are powerful and don't need to move from one state to another. The classic example is a media player. You have multiple possible states with various buttons that can change state.

For example, you are in the stopped state, and the user presses the stop button. It should do nothing and remain in the stopped state. If the user presses the play button, it should move to the playing state, and the play button should change to a pause button. Pressing the stop button should rewind the stream and move to the stopped state.

With an interaction like this, a state machine makes a lot of sense. If you don't use one, each button handler has a ton of different if statements to figure out what to do. With a state machine, you need to call this.currentState.stop() or this.currentState.playOrPause().

There are other places where state machines make a lot of sense. For example, whole libraries are dedicated to using state machines to describe UIs. https://xstate.js.org/docs/