In my experience/understanding, one's emotions are a better explanation of procrastination than a general inability to "delay gratification".

For example if you feel anxious/hopeless/overwhelmed, you might not perceive the theoretical eventual gratification as a potential outcome, or might avoid thinking much about a task at all. Seen through this lens, the subdivision trick is more of a way to manufacture a provisional gratification framework and engage with a task in a less emotionally threatening way. (With the hope that this framework can either carry you through the task or can be discarded after your negative emotions have been reduced)

I realize this doesn't directly contradict any points you made, but to me the procrastination equation doesn't feel like the most fruitful mental model of procrastination to start with.