Size of the image is relevant when processing film of course, but sensor size has become less important. I'll try find the reference to it, it was something I was reading a few days ago.
This is the flaw in your argument. Sensor size does matter - a lot, in every respect. Bigger sensors gather more light, and don't have to be magnified so much. And further, because lenses don't have to work so hard to deliver a given level of resolution from a larger image (basic MTF theory) lens performance is better too.
As I said... you take the shot differently.
There seems to be a misconception that FF gives shallower DoF and we see this repeated so many times that I just thought that it was worth saying, politely, that it simply isn't strictly true.
It is repeated many times because it is shorthand for what actually happens in practise. It is true. You have quoted Bob Atkins a lot here,
including the bit where he actually says this.
When you change anything in the imaging chain, there are knock-on effects. In terms of the DoF formula, the factors are f/number, distance, focal length and sensor size. Sensor size is expressed in the size of the Circle of Confusion, and is unrelated to pixels or film grain. If you are to make sense of these factors in practical terms, you have to establish a level playing field.
The level playing field for comparison purposes can only be the same picture, framed the same, from the same position (same perspective). If you then shoot side by side with a crop camera and full frame, at the same f/number you will get less DoF with the full framer.
I guess you might then say that in order to do that and frame the shots the same, you have had to adjust focal length. Yes, of course you have, But why was that necessary? Because the sensor sizes are different, and that's the primary driver.
Ergo, changing the size of the sensor changes the amount of DoF you get. The conversion formula is the same as the crop factor, ie with Canon, f/number x 1.6 - about one and a quarter stops difference.
