Indexing a datetime64[ns] coordinate with a scalar datetime.date produces a KeyError

Indexing a datetime64[ns] coordinate with a scalar datetime.date produces a KeyError ([6]).
Curiously, indexing with a datetime.date slice does work ([5]).
I would expect [6] to work just like [4].

This may well be related to (or a duplicate of) #3736, #4283, #4292, #4306, #4319, or #4370, but none of those actually mentions datetime.date objects, so I can't tell.

In [1]: import xarray as xr, pandas as pd, datetime as dt

In [2]: x = xr.DataArray([1., 2., 3.], [('foo', pd.date_range('2010-01-01', periods=3))])

In [3]: x
Out[3]: 
<xarray.DataArray (foo: 3)>
array([1., 2., 3.])
Coordinates:
  * foo      (foo) datetime64[ns] 2010-01-01 2010-01-02 2010-01-03

In [4]: x.loc[dt.datetime(2010, 1, 1)]
Out[4]: 
<xarray.DataArray ()>
array(1.)
Coordinates:
    foo      datetime64[ns] 2010-01-01

In [5]: x.loc[dt.date(2010, 1, 1):dt.date(2010, 1, 3)]
Out[5]: 
<xarray.DataArray (foo: 3)>
array([1., 2., 3.])
Coordinates:
  * foo      (foo) datetime64[ns] 2010-01-01 2010-01-02 2010-01-03

In [6]: x.loc[dt.date(2010, 1, 1)]
---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
<ipython-input-5-8ef314626f7d> in <module>
----> 1 x.loc[dt.date(2010, 1, 1)]

~/.conda/envs/build/lib/python3.7/site-packages/xarray/core/dataarray.py in __getitem__(self, key)
    196             labels = indexing.expanded_indexer(key, self.data_array.ndim)
    197             key = dict(zip(self.data_array.dims, labels))
--> 198         return self.data_array.sel(**key)
    199 
    200     def __setitem__(self, key, value) -> None:

~/.conda/envs/build/lib/python3.7/site-packages/xarray/core/dataarray.py in sel(self, indexers, method, tolerance, drop, **indexers_kwargs)
   1152             method=method,
   1153             tolerance=tolerance,
-> 1154             **indexers_kwargs,
   1155         )
   1156         return self._from_temp_dataset(ds)

~/.conda/envs/build/lib/python3.7/site-packages/xarray/core/dataset.py in sel(self, indexers, method, tolerance, drop, **indexers_kwargs)
   2100         indexers = either_dict_or_kwargs(indexers, indexers_kwargs, "sel")
   2101         pos_indexers, new_indexes = remap_label_indexers(
-> 2102             self, indexers=indexers, method=method, tolerance=tolerance
   2103         )
   2104         result = self.isel(indexers=pos_indexers, drop=drop)

~/.conda/envs/build/lib/python3.7/site-packages/xarray/core/coordinates.py in remap_label_indexers(obj, indexers, method, tolerance, **indexers_kwargs)
    395 
    396     pos_indexers, new_indexes = indexing.remap_label_indexers(
--> 397         obj, v_indexers, method=method, tolerance=tolerance
    398     )
    399     # attach indexer's coordinate to pos_indexers

~/.conda/envs/build/lib/python3.7/site-packages/xarray/core/indexing.py in remap_label_indexers(data_obj, indexers, method, tolerance)
    268             coords_dtype = data_obj.coords[dim].dtype
    269             label = maybe_cast_to_coords_dtype(label, coords_dtype)
--> 270             idxr, new_idx = convert_label_indexer(index, label, dim, method, tolerance)
    271             pos_indexers[dim] = idxr
    272             if new_idx is not None:

~/.conda/envs/build/lib/python3.7/site-packages/xarray/core/indexing.py in convert_label_indexer(index, label, index_name, method, tolerance)
    188             else:
    189                 indexer = index.get_loc(
--> 190                     label.item(), method=method, tolerance=tolerance
    191                 )
    192         elif label.dtype.kind == "b":

~/.conda/envs/build/lib/python3.7/site-packages/pandas/core/indexes/datetimes.py in get_loc(self, key, method, tolerance)
    620         else:
    621             # unrecognized type
--> 622             raise KeyError(key)
    623 
    624         try:

KeyError: datetime.date(2010, 1, 1)

Environment:

Reproduce the scalar datetime.date failure with the example in the issue, then inspect the label-conversion path shown in xarray/core/indexing.py, especially convert_label_indexer. Add regression coverage showing that scalar datetime.date selection works consistently with datetime selection and date slicing.