BUG: DataFrame.sort_index is not accounting for ignore_index=True for some cases

[galipremsagar]

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the master branch of pandas.

Reproducible Example

>>> import pandas as pd
>>> df = pd.DataFrame({'a': [1, 2, 3]})
>>> df.index = pd.RangeIndex(4, -1, -2)
>>> df
   a
4  1
2  2
0  3
>>> df.sort_index()
   a
0  3
2  2
4  1
>>> df.sort_index().index
Int64Index([0, 2, 4], dtype='int64')
>>> df.sort_index(ignore_index=True).index
RangeIndex(start=0, stop=3, step=1) #Index is being ignored.
>>> df.sort_index(ascending=False)
   a
4  1
2  2
0  3
>>> df.sort_index(ascending=False, ignore_index=True)
   a
4  1
2  2
0  3
>>> df.sort_index(ascending=False, ignore_index=True).index
RangeIndex(start=4, stop=-1, step=-2) # Index is not being ignored.

Issue Description

In DataFrame.sort_index, looks like ignore_index=True is being adhered to only when there is a sorting taking place. This seems to be unexpected.

Expected Behavior

The expected behavior for ignore_index=True is to always ignore the index irrespective of if there was a sorting performed or not.

Installed Versions

pd.show_versions()

INSTALLED VERSIONS

commit : 73c6825
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 : 1.3.3
numpy : 1.21.2
pytz : 2021.1
dateutil : 2.8.2
pip : 21.2.4
setuptools : 58.0.4
Cython : 0.29.24
pytest : 6.2.5
hypothesis : 6.21.3
sphinx : 4.2.0
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 : 4.10.0
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

[mzeitlin11]

Thanks for reporting this @galipremsagar! Confirmed on master, looks like ignore_index is just ignored if the sort is a noop

pandas/pandas/core/generic.py

Lines 4578 to 4582 in 72a1090

	if indexer is None:
	if inplace:
	return
	else:
	return self.copy()

Investigations to fix very welcome

[saehuihwang]

take