Look, the stuff I wrote is not my personal opinion, it is accepted fact and terminology with references.
You can't have a meaningful discussion if common facts and terminology are not accepted and understood. Too much misinformation is constantly regurgitated, the funny thing is we are talking about digital cameras, it is so easy to test this stuff for yourself it's comical.
I understand the mentality of collectors, enthusiasts, armchair pros and all manner of subdivisions of the measurebator phenomena, and there is absolutely nothing wrong to me in owning every lens and camera Canon ever made and never using any of it.
What I don't understand is the almost fanatical reluctance to actually learn what you are talking about! Why the clamor for repeating completely erroneous and incorrect opinions when the truth, even if you can't be bothered to get away from your computer for twenty minutes to actually see for yourself, is out there, just one click away.
"Can you provide an example of how reasoning in terms of angle of view may lead to errors?"
Several, just start to look into macro shooting to see where you logic completely breaks down in a common real world scenario. But the fact is that an angle of view necessitates knowing many more variables that are not related to initial dof. For instance you need to know the focal length and the sensor size to work out an angle of view, but even then without knowing subject distance you are no better off, you still can't work out dof. You don't need to know sensor size, subject distance or focal length to work out dof, just aperture and subject magnification. You can work out subject magnification by knowing sensor size, focal length and subject distance, and voila, you have a dof calculator! All it is doing with those numbers is working out subject magnification, throw in aperture and you can, eventually, work out dof.
It is like saying you need 1/250 for that exposure, well that means nothing, 1/250 at what aperture and iso? But it you tell somebody with any kind of exposure understanding "that scene is EV 10" they can work out any combination of aperture, shutter speed and iso to get the most relevant exposure for the desired image.