BUG: DatetimeIndex.strftime converts NaT to string 'NaT'

[jschendel]

Code Sample, a copy-pastable example if possible

In [1]: import pandas as pd; pd.__version__
Out[1]: '0.26.0.dev0+857.g2ade669c7'

In [2]: dti = pd.DatetimeIndex(["2019-01-01", pd.NaT])

In [3]: dti.strftime("%Y-%m-%d")
Out[3]: Index(['2019-01-01', 'NaT'], dtype='object')

This behavior carries over to Series.dt.strftime as well:

In [4]: s = pd.Series(dti)

In [5]: s.dt.strftime("%Y-%m-%d").values
Out[5]: array(['2019-01-01', 'NaT'], dtype=object)

Problem description

DatetimeIndex.strftime and Series.dt.strftime do not maintain missing values and instead coerce them to strings.

Expected Output

I'd expect NaT to get converted to np.nan.

Output of pd.show_versions()

INSTALLED VERSIONS

commit : 2ade669
python : 3.7.3.final.0
python-bits : 64
OS : Darwin
OS-release : 18.6.0
machine : x86_64
processor : i386
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 0.26.0.dev0+857.g2ade669c7
numpy : 1.16.4
pytz : 2019.1
dateutil : 2.8.0
pip : 19.1.1
setuptools : 41.0.1
Cython : 0.29.13
pytest : 4.6.2
hypothesis : 4.23.6
sphinx : 1.8.5
blosc : None
feather : None
xlsxwriter : 1.1.8
lxml.etree : 4.3.3
html5lib : 1.0.1
pymysql : None
psycopg2 : None
jinja2 : 2.10.1
IPython : 7.5.0
pandas_datareader: None
bs4 : 4.7.1
bottleneck : 1.2.1
fastparquet : 0.3.0
gcsfs : None
lxml.etree : 4.3.3
matplotlib : 3.1.0
numexpr : 2.6.9
odfpy : None
openpyxl : 2.6.2
pandas_gbq : None
pyarrow : 0.11.1
pytables : None
s3fs : 0.2.1
scipy : 1.2.1
sqlalchemy : 1.3.4
tables : 3.5.2
xarray : 0.12.1
xlrd : 1.2.0
xlwt : 1.3.0
xlsxwriter : 1.1.8