`pandas.MultiIndex` roundtrip with extension-arrays

[ilan-gold]

Is your feature request related to a problem?

In the following test

xarray/xarray/tests/test_pandas_to_xarray.py

Lines 159 to 176 in 85b5a16

	def test_to_xarray_with_multiindex(self, df):
	from xarray import Dataset
	# MultiIndex
	df.index = MultiIndex.from_product([["a"], range(4)], names=["one", "two"])
	result = df.to_xarray()
	assert result.sizes["one"] == 1
	assert result.sizes["two"] == 4
	assert len(result.coords) == 2
	assert len(result.data_vars) == 8
	tm.assert_almost_equal(list(result.coords.keys()), ["one", "two"])
	assert isinstance(result, Dataset)
	result = result.to_dataframe()
	expected = df.copy()
	expected["f"] = expected["f"].astype(object)
	expected.columns.name = None
	tm.assert_frame_equal(result, expected)

We encode that we expect extension arrays roundtripped with a MultiIndex as the dataframe index to be cast into numpy (broadcasting rules, if I remember correctly) but this should be relaxed to allow true roundtripping!

See #10559 (comment) for the originating discussion

Describe the solution you'd like

pandas.Dataframe with a MultiIndex and extension arrays in it should be roundtrippable without data type loss

Describe alternatives you've considered

N/A

Additional context

No response