The “problem” is hypercache is skipping the cache when no-cache headers are sent. This really should be disabled by default with an option to skip the cache if a no-cache header is sent because the users needing this are only going to account for fraction of those that don’t (less than 1%). Cache is’t just helpful for legitimate traffic but it helps keep server load down by harmful bots that use no-cache headers in their requests. I hope you take this into consideration.
Another problem (an actual one) is that the advanced-cache.php file throws errors if WordPress crons are executed locally using /usr/bin/php.
Notice: Undefined index: HTTP_USER_AGENT in /home/**removed**/web/www/wp-content/advanced-cache.php on line 12
Notice: Undefined index: HTTP_USER_AGENT in /home/**removed**/web/www/wp-content/advanced-cache.php on line 17
Notice: Undefined index: REQUEST_METHOD in /home/**removed**/web/www/wp-content/advanced-cache.php on line 26
Notice: Undefined index: QUERY_STRING in /home/**removed**/web/www/wp-content/advanced-cache.php on line 31
Notice: Undefined index: HTTP_HOST in /home/**removed**/web/www/wp-content/advanced-cache.php on line 129
Warning: Cannot modify header information – headers already sent by (output started at /home/**removed**/web/www/wp-content/advanced-cache.php:12) in /home/**removed**/web/www/wp-content/advanced-cache.php on line 216