I don't think even a government contractor would try such a convoluted mechanism. The computer knows the firing rate, bullet speed and dispersion, etc. It detects the missile, and tries to put a cloud of dense metal in the way. This segues into another advantage the missiles and bigger guns have--the heavier shell is more likely to penetrate the missile and make the warhead go off early.I'm guessing that the problem with the phalanx system is that the radars track the target and the stream of bullets and bring them together in an itegratting fashion. That's hard to do with a very short engagement time.
The problem with Phalanx is with the supersonic missiles. You're taking at most a third of the time to cross the engagement area, this vastly reduces the ability of the weapon to engage the missile.