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> This is exactly analogous to what you are seeing with __call__ and callable().
Your example is incorrect, __next__ is what makes an object iterable but not what makes an object have an iterator (what __iter__ does).
This correctly characterises the issue:
>>> class NonIter:
... pass
...
>>> iter(NonIter())
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
TypeError: 'NonIter' object is not iterable
>>>
>>> class DynamicNonIter:
... has_iter = False
...
... @property
... def __iter__(self):
... if self.has_iter:
... from functools import partial
... return partial(iter, [1, 2, 3])
... else:
... raise AttributeError("Not really ...")
...
>>> dni = DynamicNonIter()
>>> iter(dni)
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
TypeError: 'DynamicNonIter' object is not iterable
>>> dni.has_iter = True
>>> iter(dni)
<list_iterator object at 0x000000000362FF60>
Now, if this is possible for `iter`, why shouldn't it be possible for `callable`? 
I'm not opposed to writing a PEP but the issue with `callable` is the only one I'm aware of, and this seems too small in scope anyway.