Proposing an expansion of the definition of product() is a *completely* different issue from the validity of count() as an input. I answered correctly given the current definition of product(): it is not valid input. It is also not valid input to your proposed revision:
>>> tuple(itertools.cycle(enumerate(it)) for it in itertools.count())
...
TypeError: 'int' object is not iterable
-- just as I said.

If you want to propose an enhancement, either open an new, enhancement issue or post to python-ideas. Since new features can only go in 3.3+, post 3.x code, not 2.x. And please do not quibble about the difference between 'infinite' and 'too large to fit in memory'.