How to sort honestly
Two questions, asked in this order. Does this move something I actually care about forward? That is importance. Does it have a real deadline, one with a consequence attached? That is urgency. Most people answer the second question first, which is exactly the trap: a ringing phone and a loud inbox feel like deadlines without being attached to anything you value.
Be straight about the evidence. The matrix itself is folklore as a treatment. The Eisenhower attribution is apocryphal, and no controlled trial shows that drawing four boxes makes people more productive. What the boxes target is real and measured. In a set of experiments on the mere urgency effect, Zhu, Yang and Hsee (2018) had people choose between tasks where the urgent option paid less than the non-urgent one, and people still took the urgent option even when they could see it was worth less. The bias shrank when participants were prompted to weigh the payoff explicitly. So the useful part of the matrix is not the drawing. It is the forced pause where you name what a task is worth before you let its deadline decide for you.
The load-bearing quadrant is Schedule. Do first empties itself because deadlines push it along, and Drop is easy once you admit the item was never going to happen. Important work with no deadline is the part that quietly waits until it becomes an emergency, so it only survives if it leaves this page with a date on it. That is why the Schedule rows have a date field: pick a day, and the task moves into the scheduled list where the rest of the site can see it.
Keep the Do first quadrant small. If eight things are urgent and important, you have not sorted, you have relabelled the pile. Three is a working number, which is also the shape of the daily planner.