The issue is that the processing required in an RF system introduces a VERY brief latency (delay) in to the system. e.g. electrical signal (to fire) -> RF pulse -> translation back to electrical signal -> fire. It's a bloody fast process, but just not quite fast enough. The effect will vary by camera max sync, radio system used, etc. RF usage usually requires a slight shave off the top as it were. Using a sync cable (aargh) will give you max sync as it cuts out the RF processing and transmission part of the equation. It's just a simple mechanical switch at that juncture.
As you say, the defacto faster shutter speed effect of a fast flash duration is very dependent on what ambient exists. If you're shooting in a room that 1/200th & F_ will turn black, you're cooking. Other than the slow sync of focal plane cameras (e.g. an SLR) can pose challenges...
A short flash duration does allow for motion stoppage as it acts like a defacto faster shutter, allowing you to drag the shutter in lower light, etc as well. However, it does nothing to control ambient. The flash may only have a t=0.5 time of 1/6000 (to keep things simple) but the shutter is still open for a relatively "long" 1/200th (as an example).
Simplistic, but think of it this way:
With a t=0.5 duration of 1/6000 (0.00017 sec), the real motion-stopping duration * (t=0.1) of the strobe is more like 1/2000 (0.0005 sec). A shutter speed of 1/200 = 0.005 sec. So during that 0.005 sec the shutter is open, the flash 'controls' the scene for 0.0005 sec or 10% of it, the other 0.0045 sec the shutter is open (0.005-0.0005 sec) and allowing "in" any ambient light (plus the light from the 'tail' of your strobe pulse - think bell curve). You can you stop down to cut the effect of ambient, but this in turn requires more flash power (if available) thus dropping duration in some strobes, stretches recycle times, opens DoF, might bump you into diffraction territory, etc, etc.
Faster sync speed, as with a leaf shutter system like say a Hasselblad (1/800 sync) allows you to better wrestle ambient light into submission when using flash. It allows the use of wider apertures in brighter conditions for shallow DoF, to better underexpose a background in daylight/studio, better balance daylight with flash without nuking the area with lights or opening DoF, etc. Fashion photogs love fast sync from leaf shutter systems for these reasons.
* This pdf from Bron (starting page 9) does a great job discussing t=0.5 vs effective t=0.1 flash duration for anyone interested - followed by a lot of nice lighting gear porn ;>
http://www.bron.ch/_data/bc_do_bs_sys09_en.pdf