I'm not sure an "infinite state machine" [1] is actually a "thing" the same way a "finite state machine" [2] is a precisely defined mathematical concept in Automata Theory [3]: one level of the classes of automata more powerful than combinational logic and less powerful than pushdown automata and Turing machines.
In my mind, there is no question that finite state machines alone are not powerful enough to define practical real world user interfaces, which require the power of a Turing machine. The fact that most user interfaces incorporate many finite state machines at different levels doesn't mean that finite state machines alone are sufficient.
That's why we program browsers with JavaScript, not FSMML or FSMON.
In my mind, there is no question that finite state machines alone are not powerful enough to define practical real world user interfaces, which require the power of a Turing machine. The fact that most user interfaces incorporate many finite state machines at different levels doesn't mean that finite state machines alone are sufficient.
That's why we program browsers with JavaScript, not FSMML or FSMON.
[1] http://c2.com/cgi/wiki?InfiniteStateMachine
[2] https://en.wikipedia.org/wiki/Finite-state_machine
[3] https://en.wikipedia.org/wiki/Automata_theory