Should the page cache be refreshed often? [closed]

The one possibility is caching broken page. For example some database query fails (which is not uncommon in shared environment and/or under load) and some page gets displayed broken / with errors.

Since caching doesn’t assume integrity checking it can cache such page… And your cache interval is days – page is broken as long.

It would work better if mechanism was manual – you explicitly make something static and it remains that way (plenty CMS enginges work completely like that – generate complete static page and serve it). But I am not aware of any WP plugins that implement that.