Ok, fair enough. I have not performed extensive tests.
BUT ... I have seen enough images shot with enough lenses and cameras over the last 30 years to know in my gut that there is nothing shared across ALL nikon equipment that is somehow recognizably "nikon" and that it is this ephemeral aspect of the equipment that makes it "better" at producing "good" images than any other serious system.
There are differences between lenses and cameras ... but I'll stick by my 'nonsense' characterization until I see some evidence of this 'shared' aspect that cuts across all Nikon-branded equipment.
I'm not making the extraordinary claim that there is some Nikon magic that is better than the Canon magic ... I'm just the skeptic.
Like I said, there are differences is equipment ... but to then infer from that that 'Nikon' is better than 'Canon' simply because not all cameras and lenses are alike is nonsense.
There's a few points in your post.
Regarding the claim that Nikon has a certain magic that Canon doesn't, and hence they are better, I think most of us will agree that that is not true. And as you have said, post processing and in camera settings will make a huge difference to the final output. There is also a variation within each manufacturers lenses, some gems, some dogs, some in between.
Regarding the notion that in general manufacturers have their own style, that is hard to prove, or disprove. I use neither Zeiss nor Leica, but people who uses those brands often comment that there is a consistent difference in rendition betwen the two and also between Leica and Nikon. Is that bullshit based on "my brand is better than your brand"? Perhaps, but I hear it from some sane people. I have no direct experience of those brands so cannot comment directly. However, Canon use Flourite in many lenses, and that has particular transmission characteristics including of course a colour cast that must be balanced by careful choice of the other glass used, and coatings. Nikon will also have their own glass, with its characteristics, and their own coatings. Will that influence the result? I would expect so. To a noticeable degree? It is possible. Will some manufacturers choose glass and coatings to for example favour contrast at mid spatial frequencies? Again, it is possible.
As I have said a few times, I see obvious differences between two third party lenses I have owned, and the Nikon ones I own. Are these consistent trends? I don't know. (It is one reason I prefer to avoid third party lenses.)
But I do recall one good example that optical equipment can have a consistent 'feel' to the image. If you look at some of the old Soviet binoculars and monoculars, you will see images with a strong yellow cast, due no doubt to the choice of coatings and glass. (I suspect they were single coated with MgFl.) That is of course an extreme example, but it does show that a lens is not just transparent glass with a flat transmission spectrum in the visible wavelengths. The truth is that optical designers have a tough job to correct for the various aberrations and maintain the required colour rendition and contrast levels.