diff --git a/xarray/core/datatree.py b/xarray/core/datatree.py
index 27a2da88701..ff498a77480 100644
--- a/xarray/core/datatree.py
+++ b/xarray/core/datatree.py
@@ -156,6 +156,34 @@ def check_alignment(
             check_alignment(child_path, child_ds, base_ds, child.children)
 
 
+def _deduplicate_inherited_coordinates(child: DataTree, parent: DataTree) -> None:
+    # This method removes repeated indexes (and corresponding coordinates)
+    # that are repeated between a DataTree and its parents.
+    #
+    # TODO(shoyer): Decide how to handle repeated coordinates *without* an
+    # index. Should these be allowed, in which case we probably want to
+    # exclude them from inheritance, or should they be automatically
+    # dropped?
+    # https://github.com/pydata/xarray/issues/9475#issuecomment-2357004264
+    removed_something = False
+    for name in parent._indexes:
+        if name in child._node_indexes:
+            # Indexes on a Dataset always have a corresponding coordinate.
+            # We already verified that these coordinates match in the
+            # check_alignment() call from _pre_attach().
+            del child._node_indexes[name]
+            del child._node_coord_variables[name]
+            removed_something = True
+
+    if removed_something:
+        child._node_dims = calculate_dimensions(
+            child._data_variables | child._node_coord_variables
+        )
+
+    for grandchild in child._children.values():
+        _deduplicate_inherited_coordinates(grandchild, child)
+
+
 def _check_for_slashes_in_names(variables: Iterable[Hashable]) -> None:
     offending_variable_names = [
         name for name in variables if isinstance(name, str) and "/" in name
@@ -485,35 +513,7 @@ def _pre_attach(self: DataTree, parent: DataTree, name: str) -> None:
         node_ds = self.to_dataset(inherited=False)
         parent_ds = parent._to_dataset_view(rebuild_dims=False, inherited=True)
         check_alignment(path, node_ds, parent_ds, self.children)
-
-    def _dedup_inherited_coordinates(self):
-        # This method removes repeated indexes (and correpsonding coordinates)
-        # that are repeated between a DataTree and its parents.
-        #
-        # TODO(shoyer): Decide how to handle repeated coordinates *without* an
-        # index. Should these be allowed, in which case we probably want to
-        # exclude them from inheritance, or should they be automatically
-        # dropped?
-        # https://github.com/pydata/xarray/issues/9475#issuecomment-2357004264
-        removed_something = False
-        for name in self._indexes.parents:
-            if name in self._node_indexes:
-                # Indexes on a Dataset always have a corresponding coordinate
-                del self._node_indexes[name]
-                del self._node_coord_variables[name]
-                removed_something = True
-
-        if removed_something:
-            self._node_dims = calculate_dimensions(
-                self._data_variables | self._node_coord_variables
-            )
-
-        for child in self._children.values():
-            child._dedup_inherited_coordinates()
-
-    def _post_attach(self: DataTree, parent: DataTree, name: str) -> None:
-        super()._post_attach(parent, name)
-        self._dedup_inherited_coordinates()
+        _deduplicate_inherited_coordinates(self, parent)
 
     @property
     def _coord_variables(self) -> ChainMap[Hashable, Variable]:
@@ -1379,7 +1379,7 @@ def map_over_subtree(
         func: Callable,
         *args: Iterable[Any],
         **kwargs: Any,
-    ) -> DataTree | tuple[DataTree]:
+    ) -> DataTree | tuple[DataTree, ...]:
         """
         Apply a function to every dataset in this subtree, returning a new tree which stores the results.
 
diff --git a/xarray/tests/test_datatree_mapping.py b/xarray/tests/test_datatree_mapping.py
index c7e0e93b89b..9a7d3009c3b 100644
--- a/xarray/tests/test_datatree_mapping.py
+++ b/xarray/tests/test_datatree_mapping.py
@@ -7,7 +7,7 @@
     check_isomorphic,
     map_over_subtree,
 )
-from xarray.testing import assert_equal
+from xarray.testing import assert_equal, assert_identical
 
 empty = xr.Dataset()
 
@@ -306,6 +306,17 @@ def fail_on_specific_node(ds):
         ):
             dt.map_over_subtree(fail_on_specific_node)
 
+    def test_inherited_coordinates_with_index(self):
+        root = xr.Dataset(coords={"x": [1, 2]})
+        child = xr.Dataset({"foo": ("x", [0, 1])})  # no coordinates
+        tree = xr.DataTree.from_dict({"/": root, "/child": child})
+        actual = tree.map_over_subtree(lambda ds: ds)  # identity
+        assert isinstance(actual, xr.DataTree)
+        assert_identical(tree, actual)
+
+        actual_child = actual.children["child"].to_dataset(inherited=False)
+        assert_identical(actual_child, child)
+
 
 class TestMutableOperations:
     def test_construct_using_type(self):