I see a story about once a year about one of these which falls over and kills a child, and without any wind.

The system gets botched but can be done properly:

Link
Link

You might want to tighten up the pilaster spacing a wee bit but it's hard to imagine anyhow objecting to that.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

How do you analyze the joint reinforcing for lateral loads on the wall?
I like KootK's link that recommends not using a shelf angle so any poorly placed bricks will fall out - sort of a virtual quality control?

Yes, the "When Things Go Wrong" part is interesting, and they do acknowledge some degree of failure, reportedly due to poor site practice.

I would ask myself this question...if this single skin wall, spanning 13' between cantilevered brick beams which are reinforced with a single bar, was rotated to the horizontal, would I walk on it?

Here's some suggestions.
Brick Technical Notes No. 29A

Barret504:
A serpentine shape in plan leads to a much more stable wall. Your 4" single wythe and pilasters at 13' o/c sounds like a pretty thin and ill supported wall. Some locales in the south and southwest of the USA have their own prescriptive method of permitting and building these types of screen walls. But, as I recall the ones I’ve seen were made of a thicker, light weight conc. block which is keyed together course to course, in running bond, and then keyed into a vert. key in the pilasters which where only about 10-12' o/c. The pilasters were filled with conc. and vert. reinforcing bars. The ftgs. under the pilasters were deeper square ftgs. or piers, while the ftgs. under the wall portions were often just shovel dug trenches just below grade, for a flat, level wall building surface. Then, almost immediately, many of the builders start stretching every detail to save a few bucks per 100 ft. of wall.