Where does that energy go? Normal particles get hot and make blackbody radiation, i.e. photons.
Dark matter can't. Does it have a temperature? Can temperature flow between the particles? Without blackbody radiation you are going to have some violations of the laws of thermodynamics.
Unless dark matter has some other particle to act as an equivalent. So you are hypothesizing an entire family of dark matter particles, and a whole set of new forces.
Two entire universes each with entire sets of particles, that only interact via gravity. We could have a second sun and a second earth, that overlap us and never know it, we would just think that the gravitational constant is different (because our perceived mass is higher).
Sounds like a wonderful setting for a science fiction/horror story.