If you're not tracking, on paper, who requested what time off and when, your schedule system is not auditable and you cannot prove nepotism or favoritism easily. If you are tracking time off notifications on paper you have a formal paper trail.
Not tracking this shit benefits abuse of the time off system. Don't say “it doesn't need paperwork”, because that paperwork is your best friend in a lawsuit.
Workers should push for consistent documentation of decisions like this. Systems which cannot be audited to say exactly who requested what and when are bad systems.