First of all, it's great that you're exploring functional programming paradigms and their applicability to game programming/state management.
That being said I have to point out some things that bothered me: I believe you're conflating immutability and commutativity -- these things are not the same thing. Functional programming does not absolve you of paying attention to the order of operations. For example if you had two functions plus1 and plus2, you can order those any way you like since summation is commutative. However if you had plus1 divide2 functions, you have to pay attention to the order of application due to non-commutativity.
That being said I have to point out some things that bothered me: I believe you're conflating immutability and commutativity -- these things are not the same thing. Functional programming does not absolve you of paying attention to the order of operations. For example if you had two functions plus1 and plus2, you can order those any way you like since summation is commutative. However if you had plus1 divide2 functions, you have to pay attention to the order of application due to non-commutativity.