Since T191865 we have Due Dates for tasks.

Since T249807 I've been listing Due Dates in the weekly summary email so I can "nag" on them. I'd love not having to do this (because my time, plus I personally might annoy people while some non-individual system annoying people is better for staying friends :P ).

I probably want something™ more visible, e.g. a banner on top of phabricator.wikimedia.org for either the assignee of the non-closed task that has a Due Date in the past, or if no assignee is set for the person who set the Due Date on that non-closed ticket.

A related, though less powerful proposal is T76094: Have tasks with due dates displayed on a calendar.