The definition of builtins.iter() has it returning typing.Iterator:

The problem is typing.Iterator requires both __iter__ and __next__:

The docs for iter() does not suggest that the returned iterator must define __iter__. And if you look at the implementation of iter() -- as well as PyObject_GetIter() and PyIter_Check() which iter() uses -- there is no requirement that the returned iterator define __iter__.

All of this also applies to aiter() in regards to __aiter__.