Sure, but anything that tried to explain the observations would be a dark matter theory, and if that theory involved particles, it’d be a particle theory.

Dark matter isn’t a theory, nor is it particles, it’s just a body of observations that’s poorly named. In that sense, dark matter definitely exists, we just don’t know in what shape or form.

They don’t “communicate” faster than light, the wave function itself is non-local and collapses non-locally.

Dark matter is not a thing, it’s an observation, a phenomenon that was poorly named. There’s so much evidence under the name “sark matter” that we can’t discount it as a real phenomenon. We just don’t have a strong evidence for a single dark matter theory (theory in the scientific sense of the word, not the colloquial one).