diff --git a/pandas/core/groupby/generic.py b/pandas/core/groupby/generic.py
index b9f1ca0710872..7edd458ced790 100644
--- a/pandas/core/groupby/generic.py
+++ b/pandas/core/groupby/generic.py
@@ -345,47 +345,48 @@ def _aggregate_multiple_funcs(self, arg):
     def _cython_agg_general(
         self, how: str, alt=None, numeric_only: bool = True, min_count: int = -1
     ):
-        output: dict[base.OutputKey, ArrayLike] = {}
-        # Ideally we would be able to enumerate self._iterate_slices and use
-        # the index from enumeration as the key of output, but ohlc in particular
-        # returns a (n x 4) array. Output requires 1D ndarrays as values, so we
-        # need to slice that up into 1D arrays
-        idx = 0
-        for obj in self._iterate_slices():
-            name = obj.name
-            is_numeric = is_numeric_dtype(obj.dtype)
-            if numeric_only and not is_numeric:
-                continue
-
-            objvals = obj._values
 
-            if isinstance(objvals, Categorical):
-                if self.grouper.ngroups > 0:
-                    # without special-casing, we would raise, then in fallback
-                    # would eventually call agg_series but without re-casting
-                    # to Categorical
-                    # equiv: res_values, _ = self.grouper.agg_series(obj, alt)
-                    res_values, _ = self.grouper._aggregate_series_pure_python(obj, alt)
-                else:
-                    # equiv: res_values = self._python_agg_general(alt)
-                    res_values = self._python_apply_general(alt, self._selected_obj)
+        obj = self._selected_obj
+        objvals = obj._values
 
-                result = type(objvals)._from_sequence(res_values, dtype=objvals.dtype)
+        if numeric_only and not is_numeric_dtype(obj.dtype):
+            raise DataError("No numeric types to aggregate")
 
-            else:
+        # This is overkill because it is only called once, but is here to
+        #  mirror the array_func used in DataFrameGroupBy._cython_agg_general
+        def array_func(values: ArrayLike) -> ArrayLike:
+            try:
                 result = self.grouper._cython_operation(
-                    "aggregate", obj._values, how, axis=0, min_count=min_count
+                    "aggregate", values, how, axis=0, min_count=min_count
                 )
+            except NotImplementedError:
+                ser = Series(values)  # equiv 'obj' from outer frame
+                if self.grouper.ngroups > 0:
+                    res_values, _ = self.grouper.agg_series(ser, alt)
+                else:
+                    # equiv: res_values = self._python_agg_general(alt)
+                    # error: Incompatible types in assignment (expression has
+                    # type "Union[DataFrame, Series]", variable has type
+                    # "Union[ExtensionArray, ndarray]")
+                    res_values = self._python_apply_general(  # type: ignore[assignment]
+                        alt, ser
+                    )
 
-            assert result.ndim == 1
-            key = base.OutputKey(label=name, position=idx)
-            output[key] = result
-            idx += 1
+                if isinstance(values, Categorical):
+                    # Because we only get here with known dtype-preserving
+                    #  reductions, we cast back to Categorical.
+                    # TODO: if we ever get "rank" working, exclude it here.
+                    result = type(values)._from_sequence(res_values, dtype=values.dtype)
+                else:
+                    result = res_values
+            return result
 
-        if not output:
-            raise DataError("No numeric types to aggregate")
+        result = array_func(objvals)
 
-        return self._wrap_aggregated_output(output)
+        ser = self.obj._constructor(
+            result, index=self.grouper.result_index, name=obj.name
+        )
+        return self._reindex_output(ser)
 
     def _wrap_aggregated_output(
         self,
diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index 7fe9d7cb49eb5..cdd2cef1f2e59 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -1281,15 +1281,6 @@ def _agg_general(
                 )
             except DataError:
                 pass
-            except NotImplementedError as err:
-                if "function is not implemented for this dtype" in str(
-                    err
-                ) or "category dtype not supported" in str(err):
-                    # raised in _get_cython_function, in some cases can
-                    #  be trimmed by implementing cython funcs for more dtypes
-                    pass
-                else:
-                    raise
 
             # apply a non-cython aggregation
             if result is None: