While lighter weight and a stiffer steering assembly are definite benefits, the biggest benefit is that the setting is locked by tightening the stem, which does not affect bearing pre-load, unlike a headest with a threaded locknut. This eliminates trial and error, facilitating the process for novices and increasing profits at an LBS.
Also, the adjustments are accomplished with one small, light and inexpensive tool that can carried in a tyre sock or saddle bag in the rare event that on-road adjustment is required.
Most threadless headsets are also 1-1/8" size, so the larger diameter increases the bearing contact area, which decreases loads and increases life expectancy.
Height adjustment is not that much more difficult than a traditional quill stem. Provided the stem is left uncut, the height range can be just as large and is accomplished by moving spacers between the top and bottom of the stem.
The only arguable drawback is aesthetics and the beefy appearance can be preferable in some applications such as ATBs, frames with oversize tubes and monocoque carbon fibre frames.