I think it should be possible to break the culinary categorisation down to chemistry. That doesn’t tell you anything about the “why” but it’s definitely not random and definitely not all in our heads.
I agree with what you mean in kind of a broad-strokes way, but as individuals our subjective experiences of flavors can vary pretty wildly. There’s genetics, neurology, age, and habit/experience that influence our taste in terms of actually sensing the chemicals. Then there’s what we see, taste, and smell just prior or during tasting that severely impact our interpretation of that chemical sense.
It wouldn’t work that way. Individual Pokemon are made up of many stat values that make them much more unique than gacha characters and skins. My Espeon from Gale of Darkness can’t be replaced with another Espeon.