BUG: Performance regression to_csv when formatting datatime 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.

---

#### Code Sample, a copy-pastable example
All variants give the same output. The issue is not the different execution time of the individual variants but the performance regression of the first variant. The other variants are added just to show that nothing changed here between versions `1.1.5` and `1.2.0` (versions `1.2.1` and `1.2.0rc0` give the same results as version `1.2.0`).

```python
import pandas as pd

print(pd.__version__)

n = 100_000
df = pd.DataFrame().assign(timestamp=pd.date_range('2000',  periods=n, freq='S'), col1=1)

%timeit _ = df.set_index('timestamp').to_csv(date_format='%Y-%m-%d %H:%M:%S')
%timeit _ = df.set_index('timestamp').to_csv()
%timeit _ = df.set_index(df.timestamp.dt.strftime('%Y-%m-%d %H:%M:%S')).drop('timestamp',1).to_csv()
%timeit _ = df.to_csv(date_format='%Y-%m-%d %H:%M:%S', index=False)
%timeit _ = df.to_csv(index=False)
```

#### Problem description

Using a `date_format` for a datetime index in `to_csv` is almost 3 times slower in version `1.2.0` than in `1.1.5` (
see first row in test output: 2.39 s instead of 829 ms for 100,000 rows). For 1,000,000 rows the slowdown is 19 times.
```
1.1.5
829 ms ± 11.8 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
214 ms ± 1.12 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
987 ms ± 20.2 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
1.04 s ± 5.73 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
290 ms ± 18.6 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

1.2.0
2.39 s ± 38 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
214 ms ± 2.19 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
992 ms ± 19.2 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
1.04 s ± 4.72 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
270 ms ± 2.67 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
```
This might be related to #37484. 

<details>

INSTALLED VERSIONS
------------------
commit           : 3e89b4c4b1580aa890023fc550774e63d499da25
python           : 3.8.2.final.0
python-bits      : 64
OS               : Windows
OS-release       : 10
Version          : 10.0.18362
machine          : AMD64
processor        : Intel64 Family 6 Model 158 Stepping 10, GenuineIntel
byteorder        : little
LC_ALL           : None
LANG             : en
LOCALE           : de_DE.cp1252

pandas           : 1.2.0
numpy            : 1.19.0
pytz             : 2020.1
dateutil         : 2.8.1
pip              : 20.1.1
setuptools       : 41.2.0
Cython           : 0.29.14
pytest           : 5.4.1
hypothesis       : None
sphinx           : 2.4.4
blosc            : None
feather          : None
xlsxwriter       : 1.2.9
lxml.etree       : 4.5.0
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : 2.11.1
IPython          : 7.13.0
pandas_datareader: None
bs4              : 4.9.1
bottleneck       : 1.3.2
fsspec           : 0.7.4
fastparquet      : None
gcsfs            : None
matplotlib       : 3.3.3
numexpr          : None
odfpy            : None
openpyxl         : 3.0.4
pandas_gbq       : None
pyarrow          : 0.17.0
pyxlsb           : None
s3fs             : None
scipy            : 1.6.0
sqlalchemy       : 1.3.16
tables           : None
tabulate         : None
xarray           : 0.15.1
xlrd             : 1.2.0
xlwt             : None
numba            : 0.50.1

</details>
