In #4908 @philsward suggested that there was a need to implement the same feature to include taxonomy terms:
Taxonomies are used for a lot more than tagging content; for example they can be used as select lists. This means that currently, any taxonomies that you don't want to be indexed, have to be added as a disallow to the robots file. ... The architect could opt to remove the path field so there is no "public" alias.
In #100 we introduced a "Hide path display" checkbox in the "Display settings" tab when configuring a content type:

The Drupal version of the contrib module that offers this functionality already supports more entities:
Supported entities
This project includes sub modules that are responsible to add this behavior to different entities. The currently supported entities are:
- Nodes
- Taxonomy terms
- Users
- Files
- Field collection
- Profile 2
- Bean
You'll only need to enable the modules that you wish to add the functionality for. More entities are likely to be supported in the future. If you have a suggestion, submit a feature request using the issue queue.
I think that we should extend this feature in core to support more entities, at least taxonomy terms.
Recent comments
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.
Try using caching in the View settings, set to 24 hours. This should work for anonymous site visitors. I haven't tested this in practice, so this is just a guess.
View to show a different node each day
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