As said, we try to. Not that we managed to reach this ideal in any existing project yet. We did manage to get Auto-Save implemented without affecting the "purity" of computations, but as you said, achievements and analytics are a PITA. I think those are possible with pure computations too, but we did not yet manage to build the game architecture in a way that makes that work. Yet.

I'm currently on a research project to investigate how much of a game we can move into pure Embedded Domain Specific Languages. So, basically a set of gameplay scripting languages that enforce the "everything that happens during the frame is pure" constraint. Buuut, again, this project is still at its early stages, and under very strict budget constraints, so I cannot say yet if the outcome will be a feasible architecture or not...