Again... Kali/Escrima is a complete martial art, this particular system of KNIFE FIGHTING (I never bothered to learn the name, it was right at the start of my martial arts career and I was just anxious to learn, I don't even know if it has a name) is extraordinarily effective but limited to you having a (particular type) of knife (our knife of choice was the EK commando dagger since it had a fantastic cutting edge, a good point, a hilt and could be used with forward and back grip by left and right handers). It is one of the few techinques that I have seen capable of stopping an abaniko sequence.
I repeat: it is not a martial art, it is purely a knife fighting method that is fast and easy to learn and "too" effective.
And what's with this?
...mysterious independently developed systems that derive from Kali
As if escrima did not develop out of traditional Kali. It changed in response to the introduction of weapons and techniques by invading forces from China, Spain, etc... That is what makes Kali so effective, it's capacity to change according to circumstance, otherwise you may as well go of and learn Iaido or some of those bizarre weapons they have in Kalari Payat.
I'm with you until the end.
Iaido or Iaijutsu is the art of drawing the sword and cutting. It was never intended for street knife attacks so is irrelevant to the 'knife' discussion, albeit that it is very powerful. The last head of the school with which I studied was possibly the last man to act as kaishaku in a ritual suicidal beheading 'seppuku'. Given any long weapon - sword, stick etc, the techniques are very applicable to modern fighting.
I would, however, also argue that Kalari is much more than the sum of its weapons. A brief encounter with a Ponthi-wielding exponent in training may well be useful on the street when a machette or similar weapon is used. In escrima, would a dozen of you lie down on the floor (in random places and in random positions) in a hall and allow a blindfold exponent with a ponthi find and split the water melon you are holding ?
I'm not at all sure that I would be confident in completely debunking the Indian idea that all Chinese and Japanese martial arts derived from Kalari or at least were enhanced by it.