I guess it depends how individual exactly "set privacy for each page" ist meant to be. I would say the first step would be to make your site a walled garden site either by the Elgg core setting "for logged in users only" in the advanced site settings or by using the Loginrequired plugin (https://elgg.org/plugins/804349). Then all pages are accessible for logged-in users only as a first step (except login/register/external pages). Then you can make all these pages "public pages" (using the 'public_pages', 'walled_garden' plugin hook) that you want to be accessible for logged-out visitors, too. This should work if you don't want too many pages to be accessible. But if you want to define for example blog A as blocked but blog B, C, ... as accesible it would be not really practicable.
Security issues should be reported to firstname.lastname@example.org!