BUG: TypeError on Series(dtype='string').value_counts().idxmax()
# Expected output
Obtain the most frequent string in a series:
```pycon
>>> pd.Series('a').value_counts().idxmax()                
'a'
```

# Problem
Changing the dtype on the second example from `'object'` to `'string'` breaks this idiom:

```python-traceback
>>> pd.Series('a', dtype='string').value_counts().idxmax()
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "pandas/core/series.py", line 2168, in idxmax
    i = nanops.nanargmax(self._values, skipna=skipna)
  File "pandas/core/nanops.py", line 71, in _f
    return f(*args, **kwargs)
  File "pandas/core/nanops.py", line 924, in nanargmax
    result = values.argmax(axis)
TypeError: argmax() takes 1 positional argument but 2 were given
```
The problem is evidently not due to a `'string'` index:
```pycon
>>> pd.Series([1], index=pd.Series(['a'], dtype='string')).idxmax()
'a'
```
# Output of ``pd.show_versions()``

<details>

```
>>> pd.show_versions()

INSTALLED VERSIONS
------------------
commit           : 2a7d3326dee660824a8433ffd01065f8ac37f7d6
python           : 3.7.9.final.0
python-bits      : 64
OS               : Darwin
OS-release       : 19.6.0
Version          : Darwin Kernel Version 19.6.0: Thu Jun 18 20:49:00 PDT 2020; root:xnu-6153.141.1~1/RELEASE_X86_64
machine          : x86_64
processor        : i386
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.1.2
numpy            : 1.19.2
pytz             : 2020.1
dateutil         : 2.8.1
pip              : 20.1.1
setuptools       : 47.1.0
Cython           : None
pytest           : None
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
pytables         : None
pyxlsb           : None
s3fs             : None
scipy            : 1.5.2
sqlalchemy       : None
tables           : None
tabulate         : None
xarray           : None
xlrd             : None
xlwt             : None
numba            : None
```

</details>
