So the example I have in mind is that of a Randomised Binary Search Tree (or Treap, if you want). Its interface is pure, however it requires access to an RNG for insertions. Because of this, it cannot be treated as a pure collection: you need to tell the type system, hang on, this RBST carts around some state which changes when you insert to it, despite the fact that the state doesn't change the extensional behaviour of the structure. This is a provable property, but maybe not provable by Haskell's type system.

Now I know that you can hide unsafePerformIO in the interface, and in this case I expect it is fine, but this is not easy, it feels like a hack.

Another example that I have personally watched play itself out in disbelief was in a fairly large Haskell project: There was need of a lookup table, with some 10000 elements. In such cases, I would have stored the lookup in a database, or a separate file at least, but because they wanted to maintain purity so badly, the solution was to write a 10000 line long Haskell file. But wouldn't it be nice if you could load a file and tell Haskell: don't worry, this won't change, so treat reads to this purely.

I never said such things were impossible, merely not easy, and I don't believe this is by accident. I am almost certain that such things are made difficult to prevent abusing such features, but that doesn't stop me from missing them :) .