The quadrathlon/triathlon tests are important (along with the Power Ratio test) because they indicate where an athlete is at in terms of their speed-strength/power development, especially when compared to other athletes of roughly similar height and weight or when compared to previous results by the same athlete.  All else being equal, improvements in these tests indicate that one's physical potential for throwing far has also increased.  If an athlete's results in these tests improve along with their results in a few exercises like the front or back squat,  power clean, bench press or push press, and perhaps the power snatch, then, all else being equal, they will almost certainly throw farther.   Throwing technique is obviously essential, but this is a separate issue.  Good throwing technique is what allows an athlete to apply the power they possess in an effective manner.  Poor levels of technique result in a poor utilization of one's power, meaning that much of it is simply wasted.

The speed-strength/power tests are used in addition to tests of maximum strength because while limit strength is very important to throwers and is a vital component of speed-strength, it is ultimately speed-strength, or power, not simply limit strength, that enables one to throw far.  It is possible for someone to be very strong but slow, and such athletes do not make good throwers.  This is not a comment on any given excercise or training methodology, but a statement about abilities or outcomes.  One can argue that some exercises or training programs are more likely than others to develop high levels of speed-strength, but that is a separate issue.  If a reasonably large athlete can score in the 80th percentile in several of these tests, they are extremely powerful, regardless of what they did or did not do in their training.  Genetics can often play a very significant role, especially with respect to the speed aspect of the equation. 

The importance of one particular test or one type of test probably varies from athlete to athlete and certainly varies from event to event since speed-strength is a continuum.  For example, going from speed-dominant to more strength-dominant, we have high-jump, javelin, discus, shot put, 56# WOB, power clean, deadlift.  Javelin throwers require much more speed and much less strength than powerlifters or strongman competitors, so their training and testing must reflect that fact.