This is basically a request to merge the functionality of https://www.drupal.org/project/views_content_cache into core views:
This module implements a views cache plugin that is aware of content and can provide caching for views, until the content in those views changes.
Drupal 8 Drupal 8 has this functionality essentially baked into core, so there isn't a need for this module if your site is running Drupal 8.
Recent comments
Thanks, the /tmp folder was the problem. I moved it elsewhere and then the updated worked. Thanks again!
Update 1.35.1 appears to install but hasn't
Probably not the reason, but worth to do a quick check: Sometimes the update cache interferes, so if something's odd with updates - some module (or core) claims to have updated, but then...
Update 1.35.1 appears to install but hasn't
Nope, not touched any permissions!
Update 1.35.1 appears to install but hasn't