To try to answer the OP's question.
In the early days, I believe it was originally a backup to the main brakes. I think early brakes did tend to fail.
Now it is a back up to keep the car/truck from moving when parked.
An auto trans can slip out of gear. The parking brake (historically called the emergency brake) obviously will keep the car from rolling in the situation. Also, if parked on a hill, an auto trans can actually have enough pressure on it that you cannot take it out of park unless someone (or something) pushes it "uphill" to relieve the pressure on the transmission. If youve set the parking (emergency) brake, you wont have this problem.
I dont know if a manual trans can slip out of gear when parked. But I have heard of cases where a car has actually rolled down hill against the transmission even though it was parked in first gear or even reverse. A parking brake (that works) also guards against this.
When I was a kid, I do remember my dad stopping a car going down hill once when the brakes went out.