I like the multi-dimensional model, but it would quickly become cumbersome and complex.
The point about music being effectively a 'sub-genre' of noise, in my opinion, is arguably a more pragmatic view, and one that affords us an existing system of categorization to play with.
As for the original idea of "soundcore": There are more than enough -core's already in existence, and the creation of one to categorize an apparently vaporous, non-specific group of sound seems like more effort than it's worth.
On the other hand, why not just create your own material based on your idea of "soundcore" and then start releasing it? I did it with "Extreme Noise" (by which, I meant harsh noise, mastered to 0dB, a'la Merzbow's "Pulse Demon") on Smell the Stench, and it ended up becoming a thing on other people's releases.
If you're able to create a distinctive, unique sound that, to your ears, fulfills your criteria for "soundcore", then why not?