By using the physical aperture (iris diaphragm) diameter, you're combining (using that term loosely) focal length with aperture instead of distance. That's not wrong, but it's not the best approach because it's not universally applicable, nor is it the most convenient. I prefer easy methods that work 7 days a week, not complex methods or ones that only work on Tue-Sat.
To give the simplest case where it breaks down, consider cropping an image, which changes the DoF. It's post-capture, so you're not changing the aperture (however you define it), nor are you changing the subject distance. However, you
are changing magnification. Now, technically you can state that cropping changes the circle of confusion, because in effect you're using a smaller sensor – and that would be another correct method. But for convenience, we treat CoC as a constant for a given sensor.
Ultimately, all of these reduce to mathematical formulae, so they can be rearranged and have terms combined or separated algebraically. But I prefer magnification + aperture (+ CoC) as the simplest, most generally applicable method from a conceptual standpoint. Practically, focal length + distance + f-number (+ CoC) is probably most useful, because those three factors are what the photographer can directly control.