The spin dominance is established for ordinary matter due to the gravitational collapse to the plane of rotation. The collapse is based on losing the kinetic energy through electromagnetic interactions. Dark matter does not interact electromagnetically, does not lose the kinetic energy, and therefore does not collapse to the plane of rotation. The halo remains elliptical when it rotates, but does not collapse to a disc.
EDIT: As @rob points out in the comments, there exist a great number of elliptical galaxies.
The reason for this is the same. For the spin dominance to be established, sufficient electromagnetic interactions should be present, such as collisions (of gas, stars, dust, particles, etc.). In an ideal elliptical galaxy with only stars and vacuum, the stars do not interact electromagnetically with each other (disregarding the radiation and direct collisions), but only gravitationally similar to the dark matter particles. For this reason the stars would not lose the kinetic energy, the spin dominance would not be established, and the galaxy would remain elliptical for a long time.