BUG?: `hide_columns` now doesn't hide index names
After #43346 it is now possible to control index names visibility. This PR adds full flexibility.
This actually reverts #42839, but only because there is now an explicit method to hide index names.

Also linking this to an old master tracker #24546.

<img width="644" alt="Screenshot 2021-09-04 at 20 51 13" src="https://user-images.githubusercontent.com/24256554/132105167-f6a202c1-d2bb-4b1a-aabc-905ec1697321.png">
<img width="564" alt="Screenshot 2021-09-04 at 20 50 46" src="https://user-images.githubusercontent.com/24256554/132105172-7de05beb-d270-4792-9a86-262cc3f80660.png">

