Because that doesn't match our observations and experiments or our theories on spacetime. The 'wake' is not a wake in the sense that something is physically displacing dark matter, it is the result of gravitational interactions between the dark matter and the normal matter passing through. And we know that dark matter can't interact strongly with visible matter because we don't observe any collisions, heating, clumping, or other effects that should happen if dark matter and normal matter strongly interacted.