> We have no a priori reason to believe that matter must have multimodal interactions
No, but as a posteriori reasons go "everything else couples to the weak force" is a pretty good one.
> them dark matter is unfalsifiable
Only insofar as all the ontological content of a physical theory are unfalsifiable: you can always shift complexity around between state and dynamics if you're willing to pay the price in elegance. Consider Kaluza-Klein theory, for instance. In some sense this demonstrates that classical electromagnetism is unfalsifiable - but no one actually cares.