issue_comments: 301351084

The current behavior is actually dictated by pandas and I think it was initially intentional (before we could access MultiIndex levels as virtual coordinates).

In the first example MultiIndex.get_loc_level() is called, which doesn't return a MutliIndex:

```python In [11]: mdix = ds.yx.to_index()

In [12]: midx.get_loc_level(2, level='x') Out[12]: (array([False, True, False, False, True, False], dtype=bool), Index(['a', 'b'], dtype='object', name='y')) ```

If we want to keep the MultiIndex in this case, then I think we can just ignore new_indexes returned by indexing.remap_label_indexers and remove Dataset._replace_indexes.

But we still have to choose whether automatically renaming the dimension makes sense or not, i.e., choose between

python In [5]: ds.sel(x=2) Out[5]: <xarray.Dataset> Dimensions: (yx: 2) Coordinates: * yx MultiIndex - y (yx) object 'a' 'b' - x (yx) int64 2 2 Data variables: foo (yx) int64 2 5

and

python In [5]: ds.sel(x=2) Out[5]: <xarray.Dataset> Dimensions: (y: 2) Coordinates: * y (y) object 'a' 'b' x (y) int64 2 2 Data variables: foo (y) int64 2 5

The second issue is also due to how MultiIndex works in pandas:

```python In [10]: midx[0] Out[10]: ('a', 1)

In [11]: midx[[0, 1]] Out[11]: MultiIndex(levels=[['a', 'b'], [1, 2, 3]], labels=[[0, 0], [0, 1]], names=['y', 'x']) ```

I'm just wondering if it really makes sense to keep a MultiIndex for a coordinate that is not a dimension anymore like in this case.