Halogen is a mature technology that's reasonably cheap to implement and doesn't break the bank on power draw - unlike, say, the first few iterations of car radios. Even if there are issues during the warranty period, it's almost always blown bulbs that are relatively easy to replace.
HID was expensive to implement compared to halogen in exchange for more output and truly nominal power savings. Requires high-voltage ballasts and semi-exotic capsule construction relative to halogen bulbs. Might also want to design the housings to shield the rest of the vehicle should the capsule energetically rupture.
LED is more expensive to implement than halogen but seemingly less expensive to implement than HID, requiring simpler DC-DC circuitry and seemingly offering a smaller, more controlled emitter volume. It offers real power savings over halogen relative to HID, but we're not talking markedly smaller alternators or any other game-changing savings as a result. Naturally, the OEMs will step down to too-small wire gauges for LED and save perhaps a dollar per vehicle. From the automakers' perspective, LED will solve at least one problem that neither halogens nor HID achieve - that of commodity replacement parts undermining their parts business. They've done it with head units (try finding a standard DIN head unit in a car made within the last 10 years) so why not headlamps?
Halogen will stick around like 12V electrical systems - too much industry inertia and sunk costs around it. HID will go away to be replaced by LED as the means for selling upper-end models, higher trims, and option packages since LED is cheaper to implement, easier to mold into whatever their designers dream up, and looks to have a smaller footprint in the engine bay. Now that LED can perform adequately with single-emitter designs, I imagine it will start to creep into the lower tiers whenever the manufacturer wants to distinguish their offerings, package the engine compartment a few centimeters tighter, or try to wring some additional fractional MPG out of the design.
I do wonder if small individual LED emitters with reasonable Wheaties and compact optics will eventually be coupled into large-ish fixed arrays to attempt to achieve what some of the automakers have been doing with dynamic systems that physically move elements. With enough elements and a camera system, it should be possible to achieve similar results without futzing with moving parts and individual higher-power elements.