you have permissions to install in the base environment? or did you also create a clone?
An using
>>> conda list
…. snip ….
pywin32 223 py36hfa6e2cd_1
pywin32's description Python extensions for Microsoft Windows Provides access to much of the Win32 API, the ability to create and use COM objects, and the Pythonwin environment.
And Mark Hammond is a maintainer.
pypiwin32 also has Mark Hammon as a maintainer, but there is no description
The difference between the two packages is listed here
Re: [python-win32] pywin32 und pypiwin32: what is the difference? « python-win32 « ActiveState List ...
so I suspect the pywin32 that is distributed by esri is fine, since they don't use wheels for distribution but conda