If you are close to people or danger you may skip a few and go for the knife to cut line for instant depower(this would be very last resort).
How hard is it to control a kite with a line broken? What about control with a back line or front line break. Is there any difference in a C kite or Bow kite with a broken line?
(1) I doubt if a knife, even if it was still sharp, and even if you could get at it, would have been an option in Ken's situation, since, probably, he could not have reached an actual kite line within arm length. Cutting leader line may not be an option, but if you could, then, cutting one or two rear lines would have been a possible solution. Try a test, yourself, to see what you can reach with a kite knife, while you are hooked in.
(2) I have had a number of lines and pig tails break on "C" kites in the old days, and the kite always crashed pretty quickly. Once, a line broke, and started a cascade of other lines breaking.....only one line was left intact, and of course, that flagged the kite perfectly. One could make a case for using lower strength lines, so that, in severe conditions, where a line breaks, the domino effect would ensue, and help disable the kite. The trend in line design is in the other direction....up to 800 pound test line.
I have had the bridle break on my SLE, and the kite crashed, before I could throw it to its rear line reride safety, but I was prepared to do so.
My guess is that the most problematic kite design would be the true bow kite where the front and back lines are joined with a pulley. From what I have heard, a broken front bridal or line, with this style kite, can initiate a strong "propeller" effect, in a tight radius, where the kite may not hit the water....the more it winds up the lines, the worse it gets.
I will take a "C" kite, any day, with a broken line to deal with...in particular, a 5th line "C" kite. You have many more options to choose from, to depower a crazy kite. The best option, as you are being dragged, may be to start pulling in on your 5th line leader....5 to 10 feet of it should do the trick. I always put a 5th line on my SLE kites for this and other reasons. I have never had to do this but I have 15 feet of extra thick (quarter inch, I think) leader line on my 5th line.