Back to the original question, Why slotted headstocks?
I expect that history has a lot to do with it.
Lutes, cittens, viols and violins were all made using tapered friction pegs in a boxed headstock. The box shape gives strength to the head, as it has three solid sides. As mentioned elsewhere, it also supports and grips both ends of the tuning peg.
I expect that a slotted head came about as a cost cutting technique as, instead of carving out a hollow shape, you just need to drill a hole at each end, then saw through to join the two together. Much quicker and less skill needed.
Of course, drilling a hole through a flat piece of wood and puttting a friction peg through vertically needs fewer tools and can be done on a more basic level as shown in forerunners of the banjo, but still gave a tuneable string.
Most basic technique is simply to tie the string to the neck (tea chest bass) and tune it by a second loop tied around the neck to shorten the string - essentially capoing a single string instrument, which appears to be what is done on some African instruments (guessing from looking at pictures on the web).
Quack.
GtD.