This is how a form widget looks like for a vocabulary with nested terms, when configured to be rendered as a checkbox list:

For D7, you can use the Taxonomy Term Reference Tree Widget module to improve how this widget works, but I believe that all the bell and whistles it offers would be too much for core. We should just get rid of the dashes from the checkbox labels and add indentation to the checkboxes. It would be so much better and more readable like so:

Related: https://drupal.stackexchange.com/questions/85011/how-to-get-rid-of-the-s... https://drupal.stackexchange.com/questions/121053/add-class-to-sub-taxon... https://www.drupal.org/project/drupal/issues/648264 (Core taxonomy.module issue, pending since 2009 - although for dropdowns)
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