Actually, I just realized something based on the cool things said earlier. Let's see if I got it right.
You're saying that my shutter speed doesn't really matter as long as the flash is powerful enough for a short amount of time?
So 1/250th shutter speed + 1/4000th flash duration of suitable power would actually freeze most anything. Is that right?
If so, I got no problems with getting any of the Elinchrom gear
The question, really, is what the ambient exposure is like.
In a studio, it's generally rather dark, only lit by the dim modeling lamps. And you're generally shooting at something like 1/250 @ f/11 @ ISO 100. That's your Sunny F/16 rule, or EV 15. (I generally shoot at 1/125 @ f/8, but the difference is inconsequential.) Without the flash, the space is much closer to EV 4. You brightest highlights are below Zone I, which is why it comes out pure black.
So, what happens is that your camera flips up the mirror and opens the shutter. When the shutter is fully open, it sends the signal to the flash to fire, waits a fraction of a second (if you're shooting below your sync speed, which you should be doing), and then starts to close the shutter.
The flash duration is typically very, very, very short. So your subject is only brightly illuminated for, in your example, 1/4000 second while the flash is firing, even though the shutter is open the whole time. The rest of the time, as far as your camera is concerned, the room is pitch black.
Now, take your same setup outside on a sunny day. The ambient light is basically the same as what the flash is delivering. Even without the flash, the scene is properly exposed; with the flash, you're now overexposed.
This is where things get interesting, and why people want high speed sync. You want to reduce ambient exposure because, for whatever reason, you want the scene lit with flash and you don't want the sunlight to be contributing to the exposure. That means you're looking to set your camera to expose in the range of EV 20 or even more, which is a bit insane. You could do that with 1/1000 @ f/22 @ ISO 50, but most flashes aren't going to sync that fast at full output, you're pretty far into diffraction territory, and digital cameras aren't actually capable of exposing at ISO 50, they just clip highlights a stop faster. Realistically, you're either looking at some very unusual high-speed sync setups or neutral density filters -- and most who do that sort of thing go with the much, much cheaper and easier-to-deal-with neutral density filters.
I guess the real question is what type of motion you're looking to stop and where.
If it's outdoor sports, you don't need flash. You've got all the light you need.
If it's anything indoor and you're lighting the scene entirely with flash, the flash duration will stop the motion regardless of shutter speed.
It's only some really weird and unusual situations where you need high-speed sync to stop motion, and, if you're really in such a situation, you should prepare yourself to get down and dirty with some custom solution.