BUG:Dtypes changed from Int to Float when merging for different colunm names with Left_on Right_on outter join

[luzhideng]

• I have checked that this issue has not already been reported.

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

• (optional) I have confirmed this bug exists on the master branch of pandas.

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Note: Please read this guide detailing how to provide the necessary information for us to reproduce your bug.

Code Sample, a copy-pastable example

#Different label names 'A' and 'a'
testa = pd.DataFrame([{"A":1,"b":2}])
testb = pd.DataFrame([{"a":2,"c":2}])
result = pd.merge(testa, testb, left_on='A', right_on='a', how="outer")
result.dtypes

Out[1]: 
A    float64
b    float64
a    float64
c    float64
dtype: object

#Same lable name with on[''] methond looks fine

testa = pd.DataFrame([{"a":1,"b":2}])
testb = pd.DataFrame([{"a":2,"c":2}])
result1 = pd.merge(testa, testb, on=["a"], how="outer")

result1.dtypes
Out[2]: 
a      int64
b    float64
c    float64
dtype: object

Problem description

I was merging some df with the zipcode, so I found this might be a problem. Maybe I am wrong about this, and probably pandas designed this way for some reasons? I don't know. If anyone knows the reasons why it had built this way, please share.
I also came across with this post: #9958

Expected Output

I expecte there's no data type changes after merging.

Output of pd.show_versions()

INSTALLED VERSIONS

commit : None
python : 3.7.6.final.0
python-bits : 64
OS : Windows
OS-release : 10
machine : AMD64
processor : Intel64 Family 6 Model 61 Stepping 4, GenuineIntel
byteorder : little
LC_ALL : None
LANG : en
LOCALE : None.None

pandas : 1.0.1
numpy : 1.18.1
pytz : 2019.3
dateutil : 2.8.1
pip : 20.0.2
setuptools : 45.2.0.post20200210
Cython : 0.29.15
pytest : 5.3.5
hypothesis : 5.5.4
sphinx : 2.4.0
blosc : None
feather : None
xlsxwriter : 1.2.7
lxml.etree : 4.5.0
html5lib : 1.0.1
pymysql : None
psycopg2 : None
jinja2 : 2.11.1
IPython : 7.12.0
pandas_datareader: None
bs4 : 4.8.2
bottleneck : 1.3.2
fastparquet : None
gcsfs : None
lxml.etree : 4.5.0
matplotlib : 3.1.3
numexpr : 2.7.1
odfpy : None
openpyxl : 3.0.3
pandas_gbq : None
pyarrow : None
pytables : None
pytest : 5.3.5
pyxlsb : None
s3fs : None
scipy : 1.4.1
sqlalchemy : 1.3.13
tables : 3.6.1
tabulate : None
xarray : None
xlrd : 1.2.0
xlwt : 1.3.0
xlsxwriter : 1.2.7
numba : 0.48.0

[TomAugspurger]

You might try pandas' nullable integer dtype, which would avoid casting to floats when there aren't overlapping keys.

[peterpanmj]

Silently casting from int64 to float64 is very common, and may cause some problem (e.g people might try to downcast float64 to int64 again), I think we should raise a warning or document it somewhere