Description of the need When anonymous users are set to post comments, then additional configuration settings for anonymous commenting appear on the content type settings. Two of them allow anonymous authors to leave links to their homepages.
In most cases the field is abused by spammers who put ad links in that field. Despite it is possible to easily hide or remove the field using template overrides, I believe this field should be properly changed in core.
Proposed solution I would completely remove the field, however considering those rare websites which need visitors to leave their homepage links, we could make this configurable just in the same way as the comment titles are allowed or not like shown on the screenshot for proposed change.

Recent comments
Try using caching in the View settings, set to 24 hours. This should work for anonymous site visitors.
View to show a different node each day
That would actually be a nice usability improvement. A lot of people already build search pages with Views, so having an easier way to convert the default search results into a View would make...
[UX] Convert search to a view.
Have you already played with Views random seed? I belief, what you try to achieve would work with that module. Show only one node and set the sort order to "Global: Random seed" with "...
View to show a different node each day