BUG: `freq` attribute is `None` after `set_index`
- [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
df = pd.DataFrame({"datetime": pd.date_range("1/1/1", periods=20, freq="H", tz="UTC")})

df.set_index("datetime", inplace=True)

df.index.freq --> `None`
```


#### Problem description

This behavior is new in `1.3.0` and `1.3.1`.

In `1.2.5`, the output was, as expected, `H`

#### Expected Output

```
'H'
```

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

<details>

INSTALLED VERSIONS
------------------
commit           : c7f7443c1bad8262358114d5e88cd9c8a308e8aa
python           : 3.8.10.final.0
python-bits      : 64
OS               : Windows
OS-release       : 10
Version          : 10.0.19041
machine          : AMD64
processor        : Intel64 Family 6 Model 158 Stepping 13, GenuineIntel
byteorder        : little
LC_ALL           : None
LANG             : None
LOCALE           : fr_FR.cp1252
pandas           : 1.3.1
numpy            : 1.21.1
pytz             : 2021.1
dateutil         : 2.8.2
pip              : 21.1.3
setuptools       : 57.4.0
Cython           : None
pytest           : 6.2.4
hypothesis       : None
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : None
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : None
IPython          : None
pandas_datareader: None
bs4              : None
bottleneck       : None
fsspec           : None
fastparquet      : None
gcsfs            : None
matplotlib       : None
numexpr          : None
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : None
pyxlsb           : None
s3fs             : None
scipy            : 1.7.0
sqlalchemy       : None
tables           : None
tabulate         : None
xarray           : None
xlrd             : None
xlwt             : None
numba            : None


</details>
