Pandas Series comparison ops __finalize__ inconsistent

Looking at core.ops. _comp_method_SERIES and whether we can have the datetime and timedelta cases defer to Index subclass implementations, a couple questions come up:

https://github.com/pandas-dev/pandas/blob/master/pandas/core/ops.py#L744

    def na_op(x, y):
        # dispatch to the categorical if we have a categorical
        # in either operand
        if is_categorical_dtype(x):
            return op(x, y)
        elif is_categorical_dtype(y) and not is_scalar(y):
            return op(y, x)

This return op(y, x) looks weird. Should it be a reverse-op? e.g if op is operator.ge, should this become return operator.le(y, x)? Maybe this is irrelevant if categorical comparisons are only defined for __eq__ and __ne__? If that is the explanation, there should be a comment.

Special casing for PeriodIndex:

            if isinstance(other, ABCPeriodIndex):
                # temp workaround until fixing GH 13637
                # tested in test_nat_comparisons
                # (pandas.tests.series.test_operators.TestSeriesOperators)
                return self._constructor(na_op(self.values,
                                               other.astype(object).values),
                                         index=self.index)

I couldn't tell from #13637 what the connection was. Commenting this out did not appear to break anything in the tests. Anyone know if this is still relevant?

Update I forgot to mention the question mentioned in the Issue title. Most cases return self._constructor(res, index=self.index, name=whatever), but one case returns self._constructor(na_op(self.values, np.asarray(other)), index=self.index).__finalize__(self). Why is __finalize__ called in this case but not others?

Comment From: jreback

duplicate of #13208