BUG: combine_first() coerces to object for MultiIndex and all-nan index columns

[ssche]

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• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

>>> import numpy as np
>>> import pandas as pd
>>> df1 = pd.DataFrame({'A': [0, 0], 'B': [None, 4], 'X': pd.Series([np.nan, np.nan], dtype=float)})
>>> 
>>> df1 = df1.set_index(['A', 'X'], drop=True)
>>> 
>>> df2 = pd.DataFrame({'A': [1, 1], 'B': [3, 3], 'X': pd.Series([np.nan, np.nan], dtype=float)})
>>> df2 = df2.set_index(['A', 'X'], drop=True)
>>> 
>>> df1.combine_first(df2).index.dtypes
A     int64
X    object
dtype: object

Issue Description

df1.combine_first(df2) produces a new index with dtype object when both df1 and df2 use a MultiIndex where one of the dimensions contains all-nan values (in the example column "X").

It's expected that after combine_first() the original dtype of the index dimensions remains the same (in particular when both dataframes involved had the same dtype to begin with).

Note: this doesn't happen for a single-dimension index:

>>> df1 = pd.DataFrame({'A': [0, 0], 'B': [None, 4], 'X': pd.Series([np.nan, np.nan], dtype=float)})
>>> df1 = df1.set_index(['X'], drop=True)
>>> 
>>> df2 = pd.DataFrame({'A': [1, 1], 'B': [3, 3], 'X': pd.Series([np.nan, np.nan], dtype=float)})
>>> df2 = df2.set_index(['X'], drop=True)
>>> 
>>> df1.combine_first(df2).index.dtype
dtype('float64')

or if one of the (all-nan) index columns contains a value that is different to nan:

>>> df1 = pd.DataFrame({'A': [0, 0], 'B': [None, 4], 'X': pd.Series([np.nan, 1.0], dtype=float)})
>>> 
>>> df1 = df1.set_index(['A', 'X'], drop=True)
>>> 
>>> df2 = pd.DataFrame({'A': [1, 1], 'B': [3, 3], 'X': pd.Series([np.nan, np.nan], dtype=float)})
>>> df2 = df2.set_index(['A', 'X'], drop=True)
>>> 
>>> df1.combine_first(df2).index.dtypes
A      int64
X    float64   <---- expected result even for df1 = pd.DataFrame({... 'X': pd.Series([np.nan, np.nan], dtype=float)})
dtype: object

This issue persists for Pandas 1.5.0, 1.5.1 and 2.0.0.dev0+724.ga6d3e13b3.

Expected Behavior

No change in dtype ("X" is of type float, not object)

Installed Versions

INSTALLED VERSIONS

commit : 87cfe4e
python : 3.8.15.final.0
python-bits : 64
OS : Linux
OS-release : 6.0.8-300.fc37.x86_64
Version : #1 SMP PREEMPT_DYNAMIC Fri Nov 11 15:09:04 UTC 2022
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_AU.UTF-8
LOCALE : en_AU.UTF-8

pandas : 1.5.0
numpy : 1.23.2
pytz : 2020.4
dateutil : 2.8.1
setuptools : 59.6.0
pip : 22.3.1
Cython : 0.29.32
pytest : 7.1.2
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : 0.9.6
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : 2.8.6
jinja2 : 2.11.2
IPython : None
pandas_datareader: None
bs4 : None
bottleneck : 1.3.5
brotli : None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : None
numba : None
numexpr : 2.8.1
odfpy : None
openpyxl : 3.0.9
pandas_gbq : None
pyarrow : 1.0.1
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : 1.4.1
snappy : None
sqlalchemy : 1.3.23
tables : 3.7.0
tabulate : None
xarray : None
xlrd : 2.0.1
xlwt : None
zstandard : None
tzdata : None

[phofl]

Hi thanks for your report. This comes from MultiIndex.join

[ssche]

Oh thank you so much for the PR - I really do appreciate it!