The current feature assumed the page to always be cached, as an automated performance feature (so to speak).

But I understand there are obvious cases that this might cause issues, so it's best to make it optional.

The issue is probably related to where the module is showing content. If the module is loaded on an item page in which the item's content has not changed, then yes, it would be cached by the browser due to the headers the item itself would emit to the browser. In any case, if the caching is low, e.g. a few mins, then after that time the new content in the module would of course show up. If you're testing things though and wish to instantly see the changes but don't mind if the content loads later to actual users, then you can always hit Ctrl+R or Ctrl+Shift+R to force the browser to re-fetch the page and ignore caching headers.