BUG: Inconsistent assignment of `NAT` values to datetime columns in `MultiIndex`
- [x] I have checked that this issue has not already been reported.

- [x] 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.

---

**Note**: Please read [this guide](https://matthewrocklin.com/blog/work/2018/02/28/minimal-bug-reports) detailing how to provide the necessary information for us to reproduce your bug.

#### Code Sample, a copy-pastable example

```python
>>> import pandas as pd
>>> import numpy as np
>>> midx = pd.MultiIndex(
...         [
...             ["a", "b", "c"],
...             ["house", "store", "forest"],
...             ["clouds", "clear", "storm"],
...             ["fire", "smoke", "clear"],
...             [
...                 np.datetime64("2001-01-01", "ns"),
...                 np.datetime64("2002-01-01", "ns"),
...                 np.datetime64("2003-01-01", "ns"),
...             ],
...             [1.0, np.nan, 2],
...         ],
...         [
...             [0, 0, 0, 0, 1, 1, 2],
...             [1, 1, 1, 1, 0, 0, 2],
...             [0, 0, 2, 2, 2, 0, 1],
...             [0, 0, 0, 1, 2, 0, 1],
...             [1, 0, 1, 2, 0, 0, 1],
...             [1, 0, 1, 2, 0, 0, 1],
...         ],
...     )
>>> midx.names = ["alpha", "location", "weather", "sign", "timestamp", "float"]
>>> 
>>> pdf = pd.DataFrame({'a':[1] , 'b':[2] , 'c':[3] , 'd':[2] , 'e':[0] , 'f':[2], 'g':[10]})
>>> pdf.columns = midx
>>> pdf
alpha              a                                           b                     c
location       store                                       house                forest
weather       clouds                 storm                 storm     clouds      clear
sign            fire                  fire      smoke      clear       fire      smoke
timestamp 2002-01-01 2001-01-01 2002-01-01 2003-01-01 2001-01-01 2001-01-01 2002-01-01
float            NaN        1.0        NaN        2.0        1.0        1.0        NaN
0                  1          2          3          2          0          2         10
>>> pdf["new_col"] = [11]
>>> pdf
alpha              a                                           b                     c new_col
location       store                                       house                forest        
weather       clouds                 storm                 storm     clouds      clear        
sign            fire                  fire      smoke      clear       fire      smoke        
timestamp 2002-01-01 2001-01-01 2002-01-01 2003-01-01 2001-01-01 2001-01-01 2002-01-01     NaT
float            NaN        1.0        NaN        2.0        1.0        1.0        NaN        
0                  1          2          3          2          0          2         10      11
>>> pdf.columns
MultiIndex([(      'a',  'store', 'clouds',  'fire', '2002-01-01', nan),
            (      'a',  'store', 'clouds',  'fire', '2001-01-01', 1.0),
            (      'a',  'store',  'storm',  'fire', '2002-01-01', nan),
            (      'a',  'store',  'storm', 'smoke', '2003-01-01', 2.0),
            (      'b',  'house',  'storm', 'clear', '2001-01-01', 1.0),
            (      'b',  'house', 'clouds',  'fire', '2001-01-01', 1.0),
            (      'c', 'forest',  'clear', 'smoke', '2002-01-01', nan),
            ('new_col',       '',       '',      '',        'NaT',  '')],
           names=['alpha', 'location', 'weather', 'sign', 'timestamp', 'float'])

```

#### Problem description

It looks like just for datetime like types the `NAT` values are being inserted in multiIndex, and not for string or float types.

Previous behavior in 1.2.5 was consistent with all types, i.e., just insert empty string `''`

[this should explain **why** the current behaviour is a problem and why the expected output is a better solution]

#### Expected Output
Consistency with all dtypes as in 1.2.5

#### Output of ``pd.show_versions()``

<details>

INSTALLED VERSIONS
------------------
commit           : 5f648bf1706dd75a9ca0d29f26eadfbb595fe52b
python           : 3.8.10.final.0
python-bits      : 64
OS               : Linux
OS-release       : 4.15.0-76-generic
Version          : #86-Ubuntu SMP Fri Jan 17 17:24:28 UTC 2020
machine          : x86_64
processor        : x86_64
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.3.2
numpy            : 1.21.2
pytz             : 2021.1
dateutil         : 2.8.2
pip              : 21.2.4
setuptools       : 57.4.0
Cython           : 0.29.24
pytest           : 6.2.5
hypothesis       : 6.17.4
sphinx           : 4.1.2
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : None
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : 3.0.1
IPython          : 7.27.0
pandas_datareader: None
bs4              : 4.9.3
bottleneck       : None
fsspec           : 2021.08.1
fastparquet      : None
gcsfs            : None
matplotlib       : None
numexpr          : None
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : 5.0.0
pyxlsb           : None
s3fs             : None
scipy            : None
sqlalchemy       : None
tables           : None
tabulate         : None
xarray           : None
xlrd             : None
xlwt             : None
numba            : 0.53.1

</details>
