Should DnD combinations commute?

[JeminiZero]

I would say no. There are various instances where something might be necessary, without being commutative. Class levels are one very obvious example. E.g. at level 1, you get 4x skill points and max HP. So even with the same race and stats, a 1 fighter / 1 rogue will be very different from a 1 rogue / 1 fighter.

Another example are feats. There is a good reason why you are allowed to apply feats in whichever order is most advantageous to you, rather than in whichever order you happened to take them (or something else). Lets say you are a precocious apprentice (one level 2 spell earlier than usual). And you also happen to have a sudden metamagic. You must apply precocious apprentice feat to cast the spell first, and then you can apply the sudden metamagic to modify it. The other way round simply does not work.

All these are fundamental aspects of D&D. And since they are not commutative, I would say commutativeness is not a requirement for any combination to work.

Edit, come to think of it, even equipment is not commutative. Lets say you have a heavy sword, a weak man, and a belt of strength. Assuming the sword is too heavy for the man to pick up on his own, he must wear the belt of strength first, and then pick up the sword. Other way around doesn't work. And this is in fact a rather common occurence in computer games.