While it's far from a functional language, I find that it's possible to build functional style abstractions without too much headache. The iterator protocol is so well supported by the language and the standard libraries that using map, filter, itertools, generator expressions & comprehensions gets you a long way. You get the rest of the way by writing any specialized combinators you need and then imperative code to…
One solution would be, I think, to always pass tee-d copies of iterators and never(!) any iterator like it is (because you don't know whether next() has side effects or not). The other solution would be to not ever do anything lazy. One could also always consume all iterators fully. That way any generator re-use would be apparent immediately.
Some function that moves a generator forward just one or two items (something with the semantics of findFirst, for example), can subtly introduce bugs.