Funny thing about the check box is you check it once for the whole day.
Sure you're wide awake and alert when you show up to fly at 5pm, you may even have had a late afternoon cup of coffee. That doesn't mean you're feeling the same way later at 3am when you are landing in a snowstorm in a different time zone.
The whole idea is stupid. Self analysis must be an ongoing thing.
Better way to fight fatigue is to take turns sleeping in the cockpit during cruise. It's not officially condoned but there are plenty of advocates of "catnapping" both in the airlines and the regulating agencies. This practice needs to be condoned and encouraged along with some procedures such as having a cabin attendant check in periodically to make sure one of you is awake.