2. I didn't say the transformations can be reversed, I said if you interpret anything as an importance (e.g. a magnitude), that can be inflated / reversed by whatever weights are learned by later layers. Negative values and/or weights make this even more annoying / complicated.
3. Not sure how this is relevant, but, yes, any reasons for caring about QKV and scaled dot-product attention specifics are mostly related to performance and/or current popular leading models. But there is nothing fundamentally important about scaled dot-product attention, it most likely just happens to be something that was settled on prematurely because it works quite well and is easy to parallelize. Or, if you like the kernel smoothing explanation also mentioned in this thread, scaled dot-product self-attention implements something very similar to a particularly simple and nice form of kernel smoothing.
4. Yup, removing ops from scaled dot-product attention blocks is going to dramatically reduce expressivity, because there really aren't much ops there to remove. But there is enough work on low-rank attention, linear attentions, and sparse attentions, that show you can remove a lot of expressivity and still do quite well. And, of course, the huge amount of helpful other types of attention I linked before give gains in some cases too. You should be skeptical about any really simple or clear story about what is going on here. In particular, there is no clear reason why a small hypernetwork couldn't be used to approximate something more general than scaled dot-product attention, except that, obviously this is going to be more expensive, and in practice you can probably just get the same approximate flexibility by stacking simpler attention layers.
5. I still find that doesn't give me any clear mathematical meaning.
I suspect our learning goals are at odds. If you want to focus solely on the very specific kind of attention used in the popular transformer models today, perhaps because you are interested in optimizations or distillation or something, then by all means try to come up with special intuitions about Q, K, and V, if you think that will help here. But those intuitions will likely not translate well to future and existing modifications and improvements to attention layers, in transformers or otherwise. You will be better served learning about attention broadly and developing intuitions based on that.
Others have mentioned the kernel smoothing interpretation, and I think multiplicative interactions are the clearer deeper generalization of what is really important and valuable here. Also, the useful intuitions in DL have been less about e.g. "feature importances" and "sensitivity" and such, but tend to come more from linear algebra and calculus, and tend to involve things like matrix conditioning and regularization / smoothing and Lipschitz constants and the like. In particular, the softmax in self-attention is probably not doing what people typically say it does (https://arxiv.org/html/2410.18613v1), and the real point is that all these attention layers are trained in an end-to-end fashion where all layers are interdependent on each other to varying complicated degrees. Focusing on very specific interpretations ("Q is this, K is that"), especially where these interpretations are sort of vaguely metaphorical, like yours, is not likely to result in much deep understanding, in my opinion.