It should be obvious though that lack of focus has a negative impact to IQ
Image Quality is about how clean the image is, how well colours are reproduced, etc. Low noise and high DR contribute in a very direct fashion to IQ.
That is part of it.
As has been pointed out before, but really shouldn't need to be, there are other aspects to image quality too. Like if the subject is in focus. Indeed, in many circumstances, that is as important as noise. I'm not the first to say, though I will repeat - moderate noise can be reduced by software, but a subject cannot be made to be in focus with any postprocessing technique if it was not so in the original image.
Focus has no bearing on the image quality - only the clarity with which subject of the image is captured. An out of focus bird at ISO 25,600 is just as noisy (image data wise) as an infocus bird at ISO 25,600. Focus cannot correct image quality issues.
Yes - I'm sorry, Dilbert, but that is a bizarre attitude. You believe certain things intrinsic to an image constitute *image quality* but others don't.
Yes. Or at least I'm used to people directly referring to things such as low noise when they make statements like "wow, the Canon abcD has great IQ." It's generally got nothing to do with the composition of the image, what's been photographed or what is in or out of focus.
Look at all of the tests that websites such as dpreview do. Do they judge a camera's IQ by how well it focuses? Or do they judge it by how well a camera correctly captures and reproduces test patterns, colour charts, etc?
There seems no rationale for which, except maybe the ones Canon doesn't do as well as other manufcaturers (e.g. the much discussed low ISO DR) - which is at best contingent, and at worst constitutes deliberate bias. If I gave a number of images to a random selection of people, or entered them into a competition, and they were out of focus (except in the rare event it is an obviously deliberate/artistic choice), they would be rejected as poor. Because images are expected to be in focus - and I'd argue most people would understand the concept of focus without being taught. A noise free image that is out of focus is pretty easy to create, but unlikely to please many people.
On the other hand, many non-photographers don't really notice noise up to a certain point, and even those with exacting standards will tolerate it to varying degrees.
In competitions it is generally composition that determines whether an image is good or not, not the IQ.
Just having something in (or out of) focus is not enough to win a competition.
IQ is a property of the camera (and to some extent the lens due to CA, colour casts, etc.) It's got almost nothing to do with how easy it is to focus on a subject, etc.