bw2341 has given the right answer above, I think: Coherence of the laser light source is not relevant here. Collimation (small divergence angle) of the laser is relevant, in combination with its small beam diameter. Actually, the product of beam cross section and divergence angle, known as étendue, is the key property.
As discussed in the short video linked by bw2341 (worth watching!), étendue is preserved in a perfect optical system, and can never get smaller in a real-world system. The core DLP element can only accept a limited étendue: Its mirror array has a limited size, and the tilt angle of the mirrors limits the angle under which you can illuminate them (while still being able to separate the reflected light from the incoming illumination).
Since the component with the smallest étendue limits the optical throughput of a light path, using a light source with a large étendue -- LEDs or lamps -- together with a DLP array with small étendue will cause light losses: At some point in the beam path one has to "throw away" some of the illumination light via optical apertures, to limit its étendue to what the DLP array can accept.
That's undesirable, of course. Lasers, and even the diverging light from a small phosphor area illuminated by a laser, have smaller étendue and are hence advantageous.