There are other reasonable reasons for using Einstein's clock synchronization. Google finds, for instance
http://adsabs.harvard.edu/abs/1988AmJPh..56..811B, but if you look at the literature (including the reference list for this paper) you'll probably find that there are still some people and papers who make a rather "big deal" about clock synchronization in the literature. This has the general effect of confusing some people new to relativity, while not actually accomplishing much.
Here's my simplified "take" on the situation.
Consider taking a plane trip from New York to LA, nonstop. Ignoring take-off and landing time, you leave at 7 am, you arrive at 9 am, a two hour flight by the clock. However, by your watch, it takes you 5 hours to fly the 2000 mile distance.
On the return flight, when you leave at 7 am, you arrive at 4 pm, an 8 hour flight. But it still takes 5 hours by your watch. (I've idealized the numbers a bit, to make the example simpler).
Given that the distance is 2000 miles, is it reasonable to say that your velocity flying east from LA to NY is 2000/2 = 1000 mph, while your velocity flying from NY to LA is 2000/8 = 250 mph?
The answer, I hope, is clear - it is not "reasonable", though I suppose I should add that a sufficiently perverse and determined person can reformulate physics to work with this definition of "velocity". The point is that using this approach of allowing arbitrary clock synchronization, some reformulation of physics is needed, that this idea does not match the common, intuitive idea of what a velocity is.
For a more specific example of why physics has to be reformulated to use this defintion, consider using these "velocities" in the standard equation momentum = mass * velocity. If you do so, you will incorrectly conclude that the plane flying east has much more momentum that the plane flying west. This is testable by a rather expensive, dramatic, and unrealistic experiment of crashing one plane into another, and noting where the pieces fall. It the momenta of the two planes are equal, the pieces should be symmetrically distributed over the location of the impact - if the eastward plane has over twice the momentum of the westward plane, the pieces should fall with a large eastward bias.
What you conclude is that the cocks at LA and NY are not properly synchronized, because of "time-zones", and that (in this simplified example) the velocity of the planes flying eastward and westward are the same, i.e. 2000 mi in 5 hours, or 400 mph.
How can we make this observation more formal? We can say that, at low velocities, we expect that when clocks are properly synchronized, velocity (the distance divided by the difference in times on the lab clocks) will be equal to celerity (the distance divided by the time on a clock you carry with you). See
http://arxiv.org/abs/physics/0608040 for a definition of celerity and velocity (and thanks to robphy for finding this reference).
If we use any other scheme for synchronizing our clocks other than the standard one, we will notice the same effect that our airplane traveller does - that our velocity is not equal to our celerity even at low velocities. (Unfortunately, though, at low velocities, the experimental difference is small).
There is another way of putting this that is more readily tested in that it doesn't involve comparing almost equal numbers - rather than stating that velocity is equal to celerity at low speeds, one insists that the ratio of velocity to celerity
not depend on direction. This is in some respects the more usual approach, it is one way of approaching what people mean when they say that space-time is isotropic, i.e. doesn't have any preferred directions.
Note that we cannot directly measure the "celerity" of light, because we cannot make a clock go at the speed of light. But by using slower-than-light signals, we can come up with a means of synchronizing distant clocks that is "fair" by imposing either the requirement that celerity be equal to velocity at low velocities, or that in general the ratio of celerity to velocity must not depend on the direction in which one travels (though it can depend on the velocity).
Furthermore, we can find (and test) that this means of synchronizing clocks yields the same clock synchrnoziation as the much-simpler-to-implement method of Einstein of using light signals.
