A shared checklist is useful, but it usually stops short of the recurring ownership and reporting a household actually needs.
Checklists are static
A checklist is good for simple repeats, but it often fails to capture recurring cadence, overdue work, and visible ownership.
Task managers can show structure
A family task manager can show who owns the task, when it repeats, and what is still open.
Pick the tool that matches the problem
If your issue is simple routines, a checklist may be enough. If your issue is shared household management, you usually need more structure.