Somehow people who are in good physical health wake up each day with a certain amount of restored willpower. (This is inconsistent with the toy model in the OP, but is still my real / more-complicated model.)
This fits in with opportunity cost-centered and exploration-exploitation -based views of willpower. Excessive focus on any one task implies that you are probably hitting diminishing returns while accumulating opportunity costs for not doing anything else. It also implies that you are probably strongly in “exploit” mode and not doing much exploring. Under those models, accumulating mental fatigue acts to force some of your focus to go to tasks that feel more intrinsically enjoyable rather than duty-based, which tends to correlate with things like exploration and e.g. social resource-building. And your willpower gets reset during the night so that you could then go back to working on those high-opportunity cost exploit tasks again.
This fits in with opportunity cost-centered and exploration-exploitation -based views of willpower. Excessive focus on any one task implies that you are probably hitting diminishing returns while accumulating opportunity costs for not doing anything else. It also implies that you are probably strongly in “exploit” mode and not doing much exploring. Under those models, accumulating mental fatigue acts to force some of your focus to go to tasks that feel more intrinsically enjoyable rather than duty-based, which tends to correlate with things like exploration and e.g. social resource-building. And your willpower gets reset during the night so that you could then go back to working on those high-opportunity cost exploit tasks again.
I think those models fit together with yours.