One artificial example that can generate exponential number of states is this.

You have a list of sets and their subsets below them shown on screen. Now you take one element from one of the sets and add it to another set want things updated, this will trigger exponential computation. Since we (human) can't really visually look at all the exponential subsets anyway it will be not a very useful visulalization.

So exponential state space will be a problem only in the cases we don't care about it. Even then we could choose only few of the states by some criteria.