Requiring default index for to_feather() is unintuitive
#### Code Sample

```python
import pandas as pd
df = pd.DataFrame({'a': [1,2,3,4], 'b': [5,6,7,8]} )
df = df.drop(1)
df.to_feather("test.feather")
```
#### Problem description

I saw documentation in the code requiring default index at: https://github.com/pandas-dev/pandas/blob/794be8c7ab6897b7206f2c6ec60d22fea2e440a3/pandas/io/feather_format.py#L46-L52

However, I think it is unintuitive to require the user to have a default index before writing to feather (for example this is not a requirement to writing to csv). Why is this a requirement? What are your thoughts about reindexing being the default?

#### Expected Output

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

<details>

INSTALLED VERSIONS
------------------
commit           : None
python           : 3.6.9.final.0
python-bits      : 64
OS               : Darwin
OS-release       : 17.7.0
machine          : x86_64
processor        : i386
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 0.25.0
numpy            : 1.17.0
pytz             : 2019.2
dateutil         : 2.8.0
pip              : 19.2.2
setuptools       : 41.0.1
Cython           : None
pytest           : 5.1.0
hypothesis       : None
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : 3.8.0
html5lib         : 1.0.1
pymysql          : None
psycopg2         : 2.8.3 (dt dec pq3 ext lo64)
jinja2           : 2.8.1
IPython          : None
pandas_datareader: None
bs4              : None
bottleneck       : None
fastparquet      : None
gcsfs            : None
lxml.etree       : 3.8.0
matplotlib       : 3.1.1
numexpr          : 2.7.0
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : 0.14.1
pytables         : None
s3fs             : None
scipy            : 1.3.1
sqlalchemy       : 1.3.7
tables           : None
xarray           : None
xlrd             : None
xlwt             : None
xlsxwriter       : None

</details>
