Actually, the name is misleading. Because plying is, by definition, strands of fiber wrapped around each other, single ply yarns should really be called "not plied yarns".
Here is our culprit:
What holds yarns together, ultimately, is friction. The twist of the yarn holds the fibers together, and the friction of them rubbing together keeps the yarn from pulling apart. The more twist, the more friction, the stronger the hold, the stronger the yarn. (Unless you overtwist to the point the fibers break, but that's not today's problem.) A single ply of yarn simply doesn't have enough friction to hold itself together under stress.
That flaw explains all the problems that single ply yarns have: The pilling, general weakness, and other abrasion issues are all because there's not enough twist/friction to hold the fiber in place. That's the reason single ply yarns are 'splitty' to knit with, too.
Yes, the structure of knitted fabric CAN help hold the fibers in place. But that means knitting so tightly that any softness in the 'hand' of the yarn (how it feels) is lost. See this?
If single ply yarns suck so much, you ask, why am I knitting with one? Well, hell! Look at that color shift! I couldn't resist. But it IS splitty, and quite annoying to work with.
Why do manufacturers keep making them, then? Well, think about it. Plying adds another entire manufacturing step to the yarn making process. It uses a lot of power. Power costs money. Basically, twist is expensive. That explains not only single ply yarns, but all these under-twisted commercial yarns on the market.
If you're still interested in this topic, try "The Knitter's Book of Yarn" by Clara Parkes. She explains all this and more, in fascinating detail. :)
Now, I'm gonna go spin. I've got this glorious merino/nylon sparkle blend from Frabjuous Fibers and I can't wait to see it finished. Which means plying.