That's a feature!

Seriously though, not being able to define a serialization method can be a limitation. However, it is always possible to turn a generator into an iterator class with whatever methods you like, but the code may end up looking totally different.

To me it only looks like a limitation.

So yeah, you can write a custom class. But you will need to add a custom "save state" and "load state" in your class' __iter__ method. So all the benefits go away.