RFC: remove pandas docs pages from our doc build?

[drammock]

Personally I've never really liked the inclusion of pandas doc pages in our own docs. Given how widely used the theme is now (>6k users according to GitHub) I feel like we can trust that someone will tell us if things don't look good in their API docs, and I'm dubious as to how diligent we are at scrutinizing those pages during PR reviews anyway. I think we should remove them.

Relatedly, we've recently made a few functions from our __init__.py public, which means we really ought to document those and include them in our online docs, which would provide a similar sort of test (smaller and probably less thorough, but IMO probably still good enough). WDYT?

Originally posted by @drammock in #1307 (comment)

[timhoffm]

Note that there is also https://pydata-sphinx-theme.readthedocs.io/en/stable/examples/kitchen-sink/api.html showcasing API rendering.

[12rambau]

yep but this one's fully generated from sphinx-theme so we won't change it. The last remaining trace of Pandas api after my PR is in the real world example. as it's not relying on automodule, it should stop raising errors when pandas is updated.