Should local Ansible playbooks be loaded each day/week with cron?
I would discourage you from using Ansible to run Ansible (though this can be done) as you will run the risk of breaking idempotent rule of Ansible. Instead, choose a singular starting point for running your playbooks; either command line, cron or some other program.

With that said, I would use cron to run an Ansible playbook, however I would also setup your ansible.cfg file for logging and check the log periodically if there is breakage in your playbook.

Ansible by default doesn't do logging so I would set this up in ansible.cfg, just in case:

[defaults]
log_path = ./ansible.log


Also, make sure to check your email regularly to make sure your cron/Ansible job ran without any problem.