The twist is just old school tradition that hasn't died, and rightfully so, it does help keep the leather strap from sliding through the pedals, but also reduced rub/teeth wear on the strap from the buckle making it last a bit longer. So what they would do is put a single twist in the strap, after riding a while the teeth on the buckle would begin to wear the strap, so before they got bad, they would put another twist into the strap effectively shortening the strap which means the teeth on the buckle would bite into an area of the strap that is fresh, so they would keep doing that as time went by, and that is why you don't want to cut the strap to shorten it.
Some later pedals like Suntour Cyclone and Superbe have set screws to hold the strap in position. Those pedals would not fit regular leather straps, so nylon straps were necessary, there were some thinner leather straps but they were cheaper and wouldn't last as long.